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Fluid Physics INTRODUCTION AND OVERVIEW Study of the physics of fluid motions or, in the present context, fluid physics, is among the oldest branches of the physical sciences.* Despite this seniority, it continues to fascinate its practitioners with an eclectic collection of elegant problems. Our need to understand the world of flow around us, encompassing the nature of transport across biological membranes to the appearance of solitary waves in planetary atmospheres, remains a constant stimulation and adventure. Fluid motion, which can exhibit the randomness of turbulent flow as well as much larger-scale coherent structures, provides one of the premier testing grounds for new developments in nonlinear dynamics. We are all affected by wavelike fluid-mechanic teleconnections that transmit information about the Earth's tropical oceans over vast distances to alter patterns of global atmospheric circulation. Swimming creatures, governed by the laws of efficient underwater travel, provide insights into the evolutionary pathways stimulated by changing envi- ronments or vacant biological niches. This review of fluid physics is restricted to areas where fluid motions are of dominant importance and have only included developments in the understanding of the properties and statistical mechanics of liquids and gases that are directly related to fluids in motion. 36
FLUID PHYSICS 37 In common with many other branches of physics, fluid physics also finds a driving force in the existence of important problems in engi- neering. The pacing element for advances in many applications such as the efficiency of flight, the effectiveness of heat engines, and the productivity of chemical-processing systems is our understanding of the fundamentals of fluid motion. There are striking examples in the machines of engineering as they exist today, compared with history, that measure the magnitude of advances in our understanding of fluid physics. As it is beyond the scope of this report to catalog all of these advances, only a few will be mentioned as examples. The modern transport plane, with swept wings and quiet engines, is a reflection of the progress in the last few decades of our understanding of high-speed flows. These configurations have been derived by a combination of originally empirical and more recently theoretical and conceptual constructs, made possible by advances in our understand- ing of the physics of flow. The gas turbine engine of today, although superficially similar to its historical counterpart, includes major im- provements made possible by extensive efforts in fluid physics. Our increased knowledge of combustion and heat transfer, which were bought with so much difficulty through research, have led to lower exhaust pollution and longer life of the critical engine components. Many of today's chemical engineering plants have a throughput and an efficiency increased severalfold over those of only a decade ago, brought about by careful analysis of fluid mixing and heat transfer. These examples illustrate that basic knowledge in fluid physics moves quickly from research in flow physics to application because of the intense competitiveness of today's technological society. In the following sections of this report we review significant recent developments as well as indicate where the next decade will provide compelling advances in our understanding. There is little doubt that these advances in understanding will in turn be matched almost immediately by innovations in technology. We have also attempted to gain a useful measure of the scope and level of effort that marks this field by a review of those agencies of the government that support fluid-physics research. However, such a review cannot be exhaustive in the sense that the definitions of fiuid-physics research tend to vary significantly with the nature and mission of the funding organization, nor are we able, in the time available, to explore private industry under whose sponsorship valu- able contributions to the field have often been made. Nonetheless, these studies proved useful to the panel in its efforts to develop a series of findings with recommendations to both the funding and academic
38 PLASMAS AND FLUIDS communities, which we hope will enable us successfully to support and extend this important field of physics. In the concluding section, we found it useful to subdivide fluid physics into branches distinguished by common phenomena. While these are certainly not unique, they do offer a convenience when one is attempting to obtain a feeling for the diverse activities in the field. There are also topical subject areas that are of current and future interest but that are not clearly highlighted by subdivision into phe- nomena-related branches. As a result, selected subject or discipline areas are also highlighted when they convey more clearly the main directions in research that rely on many phenomena. Finally, there are basic technical tools that are of fundamental importance to the ad- vancement of fluid-physics research. Their status and expected devel- opment are outlined. In summary, fluid physics remains intellectually stimulating because of the natural occurrence and importance of its problems. In addition, new levels of understanding of complex phenomena have further vitalized this field. Much of this understanding has been created by the development of powerful new tools that enable us to attack the nature of complex phenomena that hitherto have appeared to be intractable mysteries. Thus, the study of turbulence, complex high-speed flows, biological flows, and geological phenomena has been paced by new developments in powerful computational and instrumentation tech- niques. We look forward to the next decade as a time of excitement, adventure, and discovery. The associated implications for the mastery of many important practical problems so necessary to the well-being of our nation and the world serve as a further stimulus. SIGNIFICANT ACCOMPLISHMENTS AND OPPORTUNITIES IN FLUID PHYSICS Significant Recent Accomplishments · The revolutionary development of computational fluid dynamics has been used to solve problems that have previously defied theoretical analysis and experimental simulation, such as convection and circula- tion within the Sun and planetary atmospheres and the nonequilibrium flow surrounding the Space Shuttle orbiter on re-entry. In conjunction with improved performance, time and costs have been reduced in the design of aircraft wings, internal combustion engines, nuclear fusion and fission devices, and surface and undersea naval vehicle compo- nents. In addition, computational fluid dynamics has increased our
FLUID PHYSICS 39 understanding of combustion, chemically reacting, and multiphase flows. · The pace of accomplishment in high-speed flows has been accel- erated by analytical methods, numerical simulation, and new experi- mental techniques. Inspired by these developments as well as by pressing social needs, significant advances have been made in the efficiency of commercial transport, manned re-entry from space, and the effectiveness of high-performance aircraft. · Recent developments have led to exciting improvements in our understanding of turbulent flows. This has enhanced our ability to compute turbulent-flow characteristics and has provided new insight into how mechanical systems can display chaotic behavior. This understanding is being brought about by new measurement techniques combined with the availability of new powerful computational tools. · Dimensional reasoning and recent theoretical understanding of jet noise, acoustic damping, and turbulent flows have led to a thousand- fold reduction in the energy of acoustic emissions from aircraft leading to major reductions in perceived noise level near airports. · Important advances have been made in our understanding of the collective behavior of dilute particulate and aerosol suspensions. New solution methods have been devised for treating large-amplitude drop- let deformation and the strong interaction between three or more particles with potential application to more dense systems. This progress has led to new insight into the behavior of clouds, fluid separation phenomena, geological magma chambers, climate dynam- ics, and complex theological fluids such as blood. · The central unifying idea of modern geology is the fluid-convection interpretation of the motion of the Earth's upper mantle. Important implications have been demonstrated for planetary evolution, earth- quakes, volcanism, and mineral and petrochemical resources. · Large-scale turbulent and coherent fluid-dynamic structures have been identified in the Earth's oceans and atmosphere and the at- mospheres of Jupiter and Venus. Their successful simulation using eddy-resolving computer models gives us a new view of laboratory turbulence and the general circulation, storms, and weather of the atmosphere and deep ocean. · Simple wavelike connections have been discovered in terrestrial climate studies. Circulation changes like E1 Nino of the tropical Pacific are communicated great distances across the globe with massive effect on rainfall and winds. · Single-photon and multiphoton excitation as well as scattering techniques have been developed to study the energy budgets of severe
40 PLASMAS AND FF UlDS gas-dynamic environments such as flames, permitting us for the first time to see inside complicated chemically reacting flows. · Noninvasive instrumentation techniques that detect blood-flow- initiated acoustic emissions from the human body, or neutrally buoyant probes that track, via satellite, the transient and mean circulation of the oceans, represent important achievements that have promoted under- standing of fluid-flow phenomena. · Fluid-dynamic modeling has led to basic new knowledge of our cardiovascular, reproductive, and urinary systems as well as many of the internal organs of our bodies and the locomotion of biological organisms from a single-ciliate cell to the hummingbird and the tuna. Fluid-dynamic principles have been vital to the design of artificial organs, cardiovascular implants, prostheses, and the development of new clinical diagnostic methods. · New constitutive models based on molecular physical structure have led to a better understanding of the striking flow properties of non-Newtonian fluids such as polymer solutions and drag-reducing agents. · The synergistic interaction of chemical, fluid, and optical physics has created the new continuous high-power laser. The success of this example has led to the identification of the importance of fluid phenomena in the performance of electric discharge and other gas- media lasers as well. Significant Research Opportunities · Rapid advancement will continue in our understanding of the characteristics and origins of turbulence, including investigations of the connection between the routes to chaos found for systems with a finite number of degrees of freedom and the continuous instability that is fluid dynamic turbulence. · As a result of the accelerating pace of physical understanding during the last decade, exciting improvements can be made in our ability to control turbulent flows and thus change their nature signifi- cantly, leading to novel drag and noise-reduction techniques; increased combustion efficiency; and control of separation, spreading, and mix- ing. Major advances in technology will be possible as a result of our ability to predict and control flows with turbulent zones. · Continued rapid growth in the development of advanced compu- tational fluid-dynamics procedures, together with the next generation of computer resources, will provide the opportunity to calculate and obtain a new level of physical understanding of complex three
FLUID PHYSICS 41 dimensional, compressible viscous flows. It will then be possible to optimize more effectively the design of high-performance aircraft, improve the forecasting of severe storm formation, attempt to predict global seasonal and annual climate changes, and realistically simulate and model fundamental processes in planetary and astrophysical fluid dynamical behavior. · Powerful laser-based optical instrumentation techniques will be developed for the rapid, multipoint measurement of flow-field proper- ties pressure, temperature, velocity, species concentration. In con- junction with rapidly developing numerical techniques, these data will be manipulated to provide new types of information as well as increase the usefulness oflargeexperimentalfacilities. · In many technologically important fluid machines the flow is either separated or unsteady or both. With the help of modern instrumenta- tion and computerized data-analysis techniques, we are beginning to understand the physics of these types of flows and how, often in combination, they can be used to improve the efficiency of technolog- ical devices ranging from heart valves to aircraft. We expect these possibilities to present a major research challenge in the coming decade. · The challenges of combustion and reacting flows are likely to yield new understanding resulting in important applications in the near future. Control of soot and other pollutants will result from understand- ing of their production mechanisms. Understanding of the interaction between chemical kinetics and fluid instabilities will result in an understanding of deflagration and the transition to detonation. Appli- cations range from improved fuel economy to fire safety. · We expect to see major advances in our understanding of multiphase flow systems, including macroscopic and microscopic interface phenomena, which are of interest in both industrial and geological processes, for example, the stability of the liquid-liquid interface leading to fingering in oil recovery, convective processes in the ocean, and the formation of layered structures in magma chambers. · There will be an increasing interest in the behavior of more-dense particulate systems, from the multiparticle interaction of finite clouds of particles to, more generally, the flow through porous media and filters based on the hydrodynamic interaction with their microstruc- ture. · Interdisciplinary cooperation in the study of basic cellular level biofluid dynamic processes in the presence of molecular forces will expedite explanations of such diverse phenomena as electrokinetic behavior in pores and membranes, the microstructure of osmosis, cell
42 PLASMAS AND FLUIDS division, cellular transport function, gel hydration, and fluid motion in intracellular tissue matrix. All lead to a better understanding of basic cellular physiological function. · Increased computational and data-handling capability will permit assimilation and understanding of the massive data sets required to describe complex natural flow phenomena as well as those in man- made devices. For example, using satellites and shipborne instru- ments, global-scale investigation is now possible of the oceans and climate dynamics. Employing Lagrangian mathematical techniques and instruments that move with the fluid, we anticipate new views of turbulent dispersion; of the interaction between waves, turbulence, and mean flow in boundary layers; and in ocean-atmosphere circula- tions. · The development of Monte Carlo computational techniques, which account for molecular motion in gas flows, will continue to be extended to higher-density flows, permitting meaningful modeling of highly nonequilibrium chemically reacting flow systems. FINDINGS AND RECOMMENDATIONS Principal Findings SUPPORT STRUCTURE · Support for basic research in fluid physics comes from a wide variety of sources. This is both a strength and a weakness, but the field suffers from the lack of an individual national identity. Despite the common technical threads that bind fluid physics, its basic research support is chaotic and limited. Considering its importance to techno- logical development and its potential for contribution to the under- standing of natural phenomena, fluid physics lacks sufficient visibility on a national scale and suffers from a lack of both amount and continuity of support from funding agencies, particularly for innovative new research directions. · Many unique national experimental and computational facilities are not readily available to a large proportion of the research commu- nity. We do recognize and applaud the U.S. government's efforts to make time available for outside research in the National Aeronautics and Space Administration's (NASA) National Transonic Facility at Langley Research Center, in the 40 ft x 80 ft wind tunnel at Ames Research Center, as well as provide computer access through the Numerical Aerodynamic Simulation Program (NASP) also at Ames, and the National Center for Atmospheric Research (NCAR) Comput
FLUID PHYSICS 43 ing Facility in Boulder. However, we believe that considerably more could be done, producing benefits for both the research community and the facilities that are involved. COMPUTATIONAL TECHNIQUES · Numerous mathematical and experimental approaches are com- mon throughout fluid physics, such as the use of asymptotic methods and laboratory flow simulations. In the last decade a new theme has emerged: the importance of the computer with applications that range from the rapid organization of data and their subsequent analysis and display all the way to the direct numerical simulation of the major features of some turbulent flows. This expanding capability provides rich opportunities for technological development and increased under- standing of natural phenomena. It is now possible to use new scientific methods to tackle important but highly complicated phenomena, such as two-phase flow, which to date have been treated primarily from an empirical point of view. The mathematical techniques that have been developed and refined during the last 15 years have become increas- ingly important tools in advancing fundamental understanding of complex flows but also importantly in improving the methods for testing the results of numerical simulations as well. In the application of numerical simulation to technological problems, and most especially to aircraft design, the Europeans have been quick to acquire the latest high-speed computers and to implement the most advanced algorithms in the design of aircraft. INSTRUMENTATION TECHNIQUES · The past decade has spawned a remarkable growth in nonintrusive laser-based flow diagnostic techniques. Combined with equally spec- tacular developments in imaging, data storage, and manipulation techniques we have, during the decade, formed the beginning of what will become unprecedented advances in flow diagnostics cooperatively coupled to computational fluid dynamics. EDUCATION · The explosive growth of fluid physics into new areas involves increasingly interdisciplinary research. Acid rain prediction, gas lasers, blood flow, and the distribution of life in the sea are examples of strong interactions of fluid physics with chemistry, physics, and biology.
44 PLASMAS AND FLUIDS Fluid systems have motivated study of bifurcation theory, Lorenz attractors, and chaos, which are prominent in the study of physics and applied mathematics. This diversity of interests can be used to unify our understanding of fundamental fluid behavior and should be a more prominent part of university education. Education and university research in fluid physics is conducted primarily in engineering and applied mathematics departments in the United States. Last year only 1 percent of the Ph.D. theses in physics and astronomy in the United States were in fluid physics, and approximately 7 percent were in plasma physics, whereas approximately 30 percent of the engineering theses were on fluid-dynamics-related projects. This low emphasis on fluid physics in our physics curriculum has deprived physics research in this country of the opportunity to participate in many areas of technology that generate exciting new fundamental problems. Principal Recommendations RESEARCH SUPPORT · We urge that a mechanism be established to provide a continuing survey of research support in fluid physics vis-a-vis the field's national and intellectual needs. While we are unable here to make a detailed suggestion about the form of this mechanism, it should provide information that will be useful in identifying basic research areas in this nationally important field that are neglected by omission or as a result of not being within the immediate sphere of influence of a support agency. Particularly, new research directions of great promise could be identified earlier. Areas that receive excessive overlapping support could also be identified. · We recommend a targeted research initiative to investigate and develop instrumentation for essentially simultaneous multipoint mea- surements of flow properties throughout large volumes. The instru- ments might be based on laser holographic methods, on multiprojection (tomographic) techniques, or on a combination of these and other as yet unexplored methods. The measurements are important to many national programs in fluid physics. It should be recognized that the instruments will be expensive, and hence it is imperative that sufficient resources be made available to the research community for their development and eventual use. · We recommend the provision of funds and organizational mecha- nisms to make unique national fluid-physics facilities available to the university and ~nongovernment communities for basic research. Direct
FLUID PHYSICS 45 allocations of time and other resources will be necessary in order to maintain an appropriate balance between basic research and urgent development programs and to assure steady operational funding of these facilities. · We strongly recommend the expansion of the role of the National Science Foundation (NSF) in supporting basic fluid-physics research, with a particular emphasis on the support available for basic fluid- physics research related to engineering science. There is funding for fluid-mechanics research embedded in the atmospheric and oceano- graphic sciences programs. However, only extremely limited funds are available for basic fluid-physics research in NSF's Engineering Direc- torate. No funds have been available from the Physics Directorate. EDUCATION · In view of the pervasive importance of fluid physics in many areas of modern technology and the numerous unexplained phenomena associated with these technologies documented in this report, we strongly recommend that physics departments in this country consider the inclusion of a required undergraduate course in fluid physics. We similarly encourage engineering schools to consider a required upper- division undergraduate course in modern physics. This would be an important step in enhancing collaborative interdisciplinary relation- ships between the physical and engineering sciences. · Fluid-flow instrumentation, especially optical techniques, are ex- pected to continue their recent exciting progress. Unfortunately this will cause the state of teaching laboratory equipment in our universities to be even more out of date. The need for dedicated, separate funding for modern laboratory equipment in fluid physics is at least as pressing as in other areas of science. · Advances in numerical simulation and experimental techniques must not obscure the fundamental importance of analytical methods. These methods have been instrumental in advancing our understanding of complex flows and an aid in the development and verification of numerical methods for computing fluid flows. GOVERNMENT SUPPORT, MANPOWER, AND UNIVERSITY RESEARCH The major agencies that support external research in fluid mechanics and combustion are the Air Force Office of Scientific Research (AFOSR), Army Research Office (ARO), Department of Energy
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FLUID PHYSICS 47 (DOE), National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Oceanographic and Atmo- spheric Administration (NOAA), and Office of Naval Research (ONR). The FY 1983 research funding levels for these agencies and other in-house activities are reviewed in Table 2.1. These numbers are of course sensitive to one's definition of basic research and should only be used as an indication of the activity in fluid physics not as a definitive compilation. For the external research support, generally about 50 percent goes to universities and 50 percent to private industry, with the exception of NSF. These support levels are approximate numbers and nominally only refer to basic research (i.e., DOD 6.1 funds). No attempt has been made to estimate the amount of contractor Independent Research and Development (IR and D) funding that perhaps should be added to these amounts. Our experience with the use of these funds leads us to believe that in practice only small amounts actually contribute to basic research. Also, no attempt has been made to characterize company and other private research in the field. An estimate of manpower in the field of fluid mechanics and combustion research can be obtained by assuming an average of $150,000 per principal investigator, which leads to a total of about 1000 full-time-equivalent principal investigators in fluid-mechanics research and about 250 in combustion research. Data from the National Bureau of Information indicate that approximately 900 Ph.D. theses are published each year in the general area of fluid dynamics. While the numbers given here are only rough approximations, they do indicate a notable national effort in the field. There are large combustion and fluid-mechanics facilities maintained by the Air Force (AECDC and WPAFB, for example), NASA (Ames and Lewis, for example), NOAA, and NSF, which do not appear in the research support levels presented above. The funding level for these facilities comes to around $250 million per year. The historical trends in support levels are of interest. These trends are shown in Table 2.2 for fluid mechanics supported by two major research funding agencies. During the same period inflation has over- whelmed the small increases in support made available. Despite the significant expenditures on fluid-physics-related activi- ties, there is only limited direct support available for innovative or discretionary university research in fluid physics. Discretionary re- search support, such as represented by the Fluid Mechanics Program in the Mechanical Engineering and Applied Mechanics Divisions of the NSF Engineering Directorate ($5.4 million per year in 1984), is very
48 PLASMAS AND FLUIDS TABLE 2.2 Historical Funding from Two Agencies for Fluid Mechanics Change in Fiscal Year · Constant Agency 1977 1978 1979 1980 1981 1982 1983 1984 Dollarsa NSFb 3.4 3.5 3.5 3.7 3.5 3.9 4.2 5.4 -who AFOSRb 9.2 9.2 10.2 11.3 11.6 12.3 -8% a Based on implicit price deflator, GNP; Business Statistics, 1982; Survey of Current Business, March 1984. b NSF Mechanical Engineering and Applied Mechanics Division, Fluid Mechanics Program, AFOSR Directorate of Aerospace Sciences. small and shrinking in terms of inflation-adjusted levels (Table 2.21. There are many areas of fluid physics that are simply-neglected by the university research community owing to a complete absence of sup- port. The large number of Ph.D. theses that are published per year in fluid physics is a result of the fact that fluid physics pervades a host of natural and man-made phenomena. They are not indicative of a high level of discretionary support for innovative, basic fluid-physics re- search. We believe that this situation is a scientific and technological mistake, with the potential for grave economic consequences. DETAILED REVIEW OF THE BRANCHES, SELECTED TOPICAL SUBJECT AREAS, AND TECHNICAL DISCIPLINES OF FLUID-PHYSICS RESEARCH In this section we have attempted to present a detailed review of fluid-physics research. First, there are fundamental-phenomena- related areas, which we call branches, that we found convenient for describing the field. Following are selected subject areas of current and future interest that we believe are topical and important but not clearly brought out by the division into branches. Finally, three technical disciplines that are of underlying importance to all of fluid-physics research are discussed. Branches of Fluid Physics COMBUSTION AND REACTING FLOWS Chemically reacting flows in general, and combustion in particular, are branches of fluid physics for which the underlying equations
FLUID PHYSICS 49 usually are considered to be the Navier-Stokes equations augmented by the equations of chemical kinetics. There are a number of aspects in which the scope of the field extends beyond this limited domain. For example, long-time correlations in kinetic theory, not described by the Navier-Stokes equations, have been inferred to affect certain turbulent ignition processes, and radiation-transport equations are needed in describing various radiant-interaction effects in combustion and radia- tion hazards from fires and explosions. However, the core of the subject is classical fluid mechanics coupled with chemical kinetics. In common with most other areas of fluid mechanics but in contrast with many other branches of physics, the underlying equations are known and the challenges are to ascertain the implications of the equations (and the values of the chemical-kinetic and transport parameters therein) for application to scientific and real-world problems of inter est. In a practical sense, combustion and reacting flows hold positions of high importance. The broad fields on which these topics have impact include those of recovery of energy resources, efficient utilization of energy resources, power sources for locomotion, atmospheric pollu- tion, chemical lasers, waste disposal, and safety hazards. Numerous examples of relevance to these areas can be cited. Underground combustion, both reverse and forward, provides a potential means for large-scale recovery of oil from oil shale and of energetically useful gases from coal. Economies and improved efficiencies in natural gas, oil, and coal burners are achievable to some extent through advances in the understanding of combustion processes. Chemically reacting flows are of central relevance in the chemical process industries and in fuel refining. Emissions of oxides of nitrogen, of unburned hydrocar- bons, and of soot and other particulates from both mobile and stationary power sources could be reduced by more rational means if better knowledge of salient combustion processes were available. Novel methods for disposal of hazardous wastes by incineration rely on knowledge of the fluid mechanics of the combustion processes involved. Fires are an ever-present threat to health and safety that necessitate continuing research on chemically reacting flows, e.g., to combat dangers associated with the rapidly changing mix of combus- tible materials in the modern urban environment. Importation of liquefied natural gas in large volumes has spurred research on the fire and explosion hazards of combustible clouds. Even nuclear reactors exhibit unique combustion hazards, as the Three-Mile Island incident demonstrated. Although this list specifically calls out practical prob- lems, there are many scientifically challenging problems in the area that
50 PLASMAS AND FLUIDS are not tied directly to applications; moreover, improved scientific understanding increasingly is becoming a useful means for addressing the practical problems cited. There are a number of significant recent developments in the area of combustion and reacting flows. In studies of burning of individual fuel droplets, conditions have been measured and largely understood under which a bubble is generated and grows within the liquid, shattering the droplet and in the process producing more efficient combustion with less production of soot and oxides of nitrogen. Modern diagnostic experiments, computational methods, and analytical methods together have given greatly improved knowledge of structures and propagation mechanisms of premixed laminar flames, thereby offering ideas, for example, for achieving reliable combustion under highly fuel-lean conditions in spark-ignition engines to improve performance. Signifi- cant improvements in the understanding of laminar-flame instabilities have been achieved, including interactions of hydrodynamic, diffusive, and gravitational phenomena to shed light on the reasons why Landau's classical prediction of absolute instability does not conform with experiment. Novel methods for calculating heat-release rates and rates of production of oxides of nitrogen in turbulent diffusion flames have been developed, contributing to understanding of possible meth- ods for reduction of pollutant production. Improved understanding of extinction of diffusion flames has been achieved and applied to problems of flame stabilization and fire suppression. The first steps have been taken toward the development of rational descriptions of premixed turbulent-flame propagation, so that prospects exist for the emergence of a correct fundamental understanding of this intricate process. A number of recent developments in theory and experiment on flame spread along surfaces of fuels have improved our knowledge of mechanics of fire spread and led to new ideas on fire safety. Plenty of problems remain, and useful new methods for attacking them continue to be developed. The quality and number of young research- ers in the area are increasing. Great challenges in combustion and reacting flows that are likely to be met and overcome at least partially in the near future may be listed as follows: · Develop an understanding of mechanisms of flame propagation in areas ranging from fuel recovery to power production to fire safety. · Develop descriptions of complex chemical-kinetic processes such as soot production that are simple and accurate enough to enable their overall rates and their influences on laminar-flame structures and dynamics to be understood and calculated.
FLUID PHYSICS 51 · Develop firmly based and reliable methods for describing struc- tures and propagation speeds of premixed turbulent flames, applicable to real combustors of practical importance. · Clarify influences of chemical kinetics and chemical mechanisms on instabilities of reactors and flames. · Develop improved descriptions of burning of sprays, including specifications of combustion regimes and more understanding of influ- ences of turbulence. · Demonstrate explicitly how pressure waves develop and interact in thermal explosions, in deflagration propagation, and in processes of transition to detonation. · Clarify the relative importance of phenomena contributing to limits of flammability and of detonability, and describe near-limit propagation mechanisms better. · Ascertain the relative importance of chemical and physical phe- nomena in contributing to flame extinction by different agents. The list could be extended. In general, a broad range of methods, theoretical and experimental, must be brought to bear in finding solutions to these problems. NON-NEWTONIAN FLUIDS AND RHEOLOGY For over a hundred years, it has been customary in fluid mechanics to accept the Newtonian constitutive equation, i.e., the proportionality between stress and rate of deformation, as the standard fluid model that in conjunction with the laws of mechanics leads to the well-known Navier-Stokes equations of motion. Yet it has become increasingly apparent in recent years that there exist a great many fluids whose flow behavior differs in such a striking and fundamental way from that of their Newtonian counterparts that new constitutive equations need to be developed in order to properly model such systems theoretically. Examples of such fluids are blood, slurries, molten plastics, emulsions, suspensions of fibers, pastes, foams, and polymer solutions, so that it is being recognized that Newtonian behavior is the exception rather than the rule for a large class of substances having practical impor- tances in a wide range of industrial processes. Considerable effort has therefore been expended in an attempt to construct constitutive equations that relate the stress to the rate of deformation for such non-Newtonian materials, and indeed a large number of such equations have been proposed by various investiga- tions. Unfortunately, these equations are, as a rule, quite complicated,
52 PLASMAS AND FF UlDS and it is far from clear at this stage which of them, if any, can properly account for the multitude of the observed non-Newtonian phenomena. Thus, an increasing amount of attention is currently being directed at evaluating the usefulness and applicability of existing constitutive equations rather than constructing new ones. This, however, is not an easy task, for, even when inertia can be neglected- which in the corresponding Newtonian case renders the Navier-Stokes equations linear the resulting mathematical expressions are still nonlinear, owing to the complicated form of the constitutive equations, so that they can be tackled only via numerical techniques if the problem is anything but very simple. Even so, difficulties remain to be overcome. Since the system of equations for the non-Newtonian fluids is, in general, higher order than for the Newtonian case, additional boundary conditions are needed that, however, are not always obvious. Also, questions regarding existence or uniqueness of the solution to the mathematical system as posed need to be addressed in conjunction with the numerical computations. A dimensionless parameter that often plays a crucial role in deter- mining the flow behavior of a non-Newtonian visco-elastic fluid is the Weissenberg number W. which is defined as the ratio of the relaxation time of the fluid to the characteristic time of the flow and which provides a measure of the non-Newtonian character of the system. Unfortunately, it has generally been found that conventional iterative numerical techniques fail to provide a solution to the appropriate set of equations and boundary conditions beyond a relatively low value of W. where the velocity field shows little difference from its Newtonian counterpart. It is not known at present whether the failure of these numerical solutions is due to deficiencies in the numerical schemes or whether it results from the mathematical problem having been ill- posed. Certainly, the resolution of this question is currently an important problem in this area of research. Another non-Newtonian phenomenon, which is fundamentally dif- ferent from everything that has been referred to above, is that of drag reduction, wherein it is found that the addition of certain macromole- cules in minute concentrations (parts per million) to Newtonian fluids (typically water) can significantly reduce the pressure drop in pipes under turbulent flow conditions even though, in a viscometer, these solutions behave as Newtonian substances having virtually the same viscosity as the solvent. Drag reduction is therefore not only of obvious practical importance it has already been employed in the Alaska pipeline as well as in many other instances but the explanation of its origin would go a long way toward helping us to understand the
FLUID PHYSICS 53 phenomenon of turbulent shear flow, which is currently the most important unsolved problem in fluid mechanics. Despite intensive effort on this topic, the factors that control this observed drag reduction are still not completely understood. From a fundamental point of view, however, the key missing ingredient that inhibits rapid progress in this field is our incomplete understanding of the physics of non-Newtonian fluids and in particular the relationship between their physical constitution and their rheologi- cal behavior. A promising avenue for research that is currently being pursued involves constructing constitutive equations based on our detailed knowledge of the microscopic structure of the fluid, as is the case for polymer solutions, emulsions, and suspensions. Such an example is the "reptation" theory recently developed by deGennes and by Doi and Edwards. If successful, this approach should provide us with an in-depth understanding of the striking flow properties of non-Newtonian fluids-which are often very unlike those observed with Newtonian substances and even help us to discover new non- Newtonian phenomena or construct fluids with preassigned flow char- acteristics. VORTEX-DOMINATED FLOWS The study of vortex-dominated flow fields aims to describe situa- tions, steady or nonsteady, in which the velocity induced by strong vorticity is the central feature in establishing the flow field itself. Such flows are intended to contrast with those where, for example, weak vorticity is transported by a strong Notational flow, and hence, to a considerable extent, the problem may be considered a linear one. Familiar examples are thin airfoil theory, lifting line theory, and most lifting surface theory. Examples of nontrivial but well-known vortex- dominated flows are the vortex pair and the vortex ring. Several classes of vortex-dominated flows are described below according to the physical origin and interest of specific problems rather than from the standpoint of their analytical or computational diffi- culties. Disturbance of Initially Rotational Fields A wide variety of problems involve an initially strong vertical field that is disturbed by boundaries or body forces. A classical example of such a physical situation is the flow produced by a finite wing moving through a strongly rotational field, studied initially by Karman and
54 PLASMAS AND FLUIDS Tsien. This phenomenon appears to be of great current importance in the behavior of blades in the compressor and turbine components of aircraft gas turbines. Another important example under active devel- opment is the flow of initially rotational fluids in ducts and channels having complex bends and changes in shape of their cross section. This general field has become known as secondary flow and is of great interest in the investigation of ducts leading to the inlets of aircraft gas turbine power plants. Vortex Fields Generated by Highly Loaded Wings and Bodies One of the most spectacular and important examples of vortex- dominated flows arises in the flow fields generated by highly loaded wings and by bodies at high angles of attack. Both research workers and designers have accommodated their intuition and understanding to the simplifications and results of lightly loaded wing and body theory, but frequently the fields of heavily loaded wings and bodies bear little resemblance to their classical counterparts. The tendency of the strong vorticity shed from heavily loaded wings to roll up quickly into rather concentrated vortex tubes leads to unusual trajectories, intense in- duced velocity fields, and frequently to asymmetric or nonsteady flow patterns and forces. The understanding and description of these complex flow fields is one of great importance in estimating the performance of high-speed aircraft, particularly high-performance fighters. In many practical instances the situations described above involve three-dimensional flow separation, and, as is well known, the tendency for an asymmetric flow to be associated with a symmetric geometric configuration is aggravated. The influence of the strong vortices on the separation line becomes a central issue. Diligent and continuous research, both experimental and theoretical, is required to achieve an acceptable degree of quantitative understanding. Geophysical Flows Important flow patterns as they occur in the atmospheres of the Earth and other planets may be considered as vortex dominated. Among the important members of this group are the general problem of weather prediction, tornadoes, fire storms, and possible weather modification. The details of geophysical flows are covered elsewhere in this report.
FLUID PHYSICS 55 Contained Vortices The ability of many practical devices to function is dependent on the generation and stabilization of vortices or groups of vortices within fixed geometric boundaries. Centrifuges, ultracentrifuges, small parti- cle separators, and the vortex containment of nuclear reactions are familiar examples. In other circumstances the vortices occur inadvert- ently; an interesting example is the formation of a strong axial vortex in some solid propellant rocket motors, the effects of which may lead to dynamic instability of a missile. HIGH-SPEED FLOWS There are several opportunities for major advances in high-speed flows that extend the developments of the past decade. These past developments have been focused in two primary technology areas. One is the development of highly efficient commercial and military trans- port; the other is the development of highly maneuverable fighter aircraft. These developments will continue primarily from advances in our understanding of separated flows, from our special knowledge of new aerodynamic design procedures, from our beginning understand- ing of, and thereby our ability to control, turbulence, and from the continuing growth in the use of computers to solve aerodynamic flow fields (addressed elsewhere). In many flows of technological interest the flow is either separated or unsteady or both. We are beginning to understand the fundamental physics of these separated and unsteady flows and how, often in combination, they can be used to improve the efficiency and perform- ance of technological devices. Both steady and unsteady mechanisms can be used to generate separated flows. These separated flows have special characteristics that have made them important in the design of supersonic aircraft. We are just beginning to understand the nature of the separation process, the fundamental physics of these flows, and how they can be generated and utilized through unsteady surface motions. We are now beginning to understand better the fundamental physics of the process of transition to turbulence, and through that understand- ing we are beginning to develop controls that suppress this transition. These controls range all the way from acoustic input to the boundary layer through the removal of a substantial portion of boundary layer from the surface.
56 PLASMAS AND FLUIDS It has been known for some time that the aerodynamic designs that operate at high subsonic Mach numbers are most efficient if they can avoid the generation of shock waves. But such flows are mathemati- cally isolated from one another and were, for some time, thought to be impractical. It has been demonstrated over the last decade that these mathematically isolated solutions are of practical value, and special techniques have been developed to find them. These techniques have now been generalized to the point where they can be used routinely in the design process, guaranteeing that the extremes of the transonic design envelope can be reached. By the end of the century we can expect a significant increase in the fuel economy of the present-day commercial aircraft. This increase will occur through a number of design innovations, and the aerodynamics of high-speed flow will contribute roughly 20 percent of this improve- ment. For this reason alone, the fundamental physics of these flows is especially important. In addition, there are many devices whose designs may be altered radically if one turns from steady attached flows to unsteady separated flows to improve their performance. Our under- standing of the physics of these unsteady separated flows is just beginning and is especially important. MOLECULAR AND STATISTICAL PHENOMENA Molecular-scale phenomena are basic to all of fluid mechanics. Transport properties such as diffusion coefficients, interface transport phenomena, and non-Boltzmann energy-level population distribution in chemically active flows are examples. In the past decade one of the developments in this area has had an important influence on chemical physics. Flow cooling, or the expan- sion of a sample and a carrier gas through a nozzle to millikelvin temperatures, has been developed based on aerodynamic molecular- beam techniques. A rapidly increasing momentum-transfer-collision cross section at low temperatures, which overwhelms the density decrease due to the expansion, allows collisions to be active through- out the flow. The very low gas-phase temperatures that are achieved permit studies of collisions between isolated energy states through state-selective excitation of crossed molecular beams. There have been notable recent advances in statistical phenomena related to biological problems. Phenomenological coefficients in the Kedem-Katchalsky equations (equations coupling water and solute movement across biological membranes) have been derived from more fundamental equations describing diffusion and convection in biologi
Ff UlD PHYSICS 57 cat pores. The role of endothelium as a transport barrier for macro- molecules has been elucidated through the use of quantitative models to examine the change in arterial wall permeability to cell turnover (dying of endothelial cells), vesicle transport, and the opening of the intercellular junctions between cells. The models have been used to explain why minute changes in endothelial structure can lead to localized regions with twofold increase in lipoprotein uptake. Another subject that has received attention in the past, but now appears particularly ready for rapid development, is the use of Monte Carlo techniques for handling gas flows at relatively high pressures with detailed accounting of internal-energy-state transitions. Appropri- ate collision probabilities can be generated or verified by the selected- state chemistry studies described above. Advances here would be an important step in describing highly nonequilibrium chemically reacting flows, which are important in applications such as high-energy chem ical lasers. We expect that there will be exciting developments in the biological application of statistical phenomena. Osmosis has still only been explained from a macroscopic thermodynamic viewpoint. A micro- scopic theory on the length scale of the membrane pore diameter is still needed. There is also no microhydrodynamic theory describing the transition from deterministic to diffusion-dominated particle motion (particles with diameters of 100 to 1024 A). In general, problems in biological transport of water, ions, and macromolecules involve novel boundary conditions for the surface layer of epithelial and endothelial cells, difficult problems in subendothelial interaction, and a variety of new phenomena such as endocytosis and exocytosis associated with the biophysics of the plasma membrane of the individual cells. VISCOSITY-DOMINATED FLOWS The area of viscous fluid mechanics where the primary force balance on a fluid element is between pressure and viscous stresses and the inertia of the fluid element is small is often referred to as low-Reynolds- number hydrodynamics. This basic force balance is satisfied in a wide variety of applications involving multiphase flow, thin films, molecular diffusion, interface phenomena, and colloid and membrane science. Stimulated by the work of G.I. Taylor on the swimming of micro- organisms, many of the newer problems in low-Reynolds-number fluid motion have been motivated by biological applications. This includes such diverse problems as the swimming of sperm and other flagellar or ciliated organisms; the movement of the cellular components of blood
58 PLASMAS AND FLUIDS in the microcirculation; the motion of fluid or particles in biological ducts lined with cilia such as the oviduct, the small intestine, or the intestine; trachea; and the gaseous exchange in lung alveoli. During the past decade interest in low-Reynolds-number hydrody- namics has grown tremendously, spurred by numerous applications in the chemical processing industries, new biological problems, and the advent of numerical solution techniques that could treat a much wider variety of particle- and boundary-interaction problems than could be handled by purely analytical methods. The chemical processes involve such problem areas as modern filter technology, aerosols and sprays, sedimentation of particles and colloidal suspensions, fluid-fluid sepa- ration processes, electrokinetic and osmotic phenomena, hydrody- namic chromatography, surfactant technology, and molecular trans- port through biological and synthetic membrane es. The new biological applications derived from the need to obtain better understanding of a variety of cellular level biological phenomena, such as the vesicular transport of lipoproteins across arterial endothelium (thought to be related to arterial disease), the deformability of cells due to fluid motion, and the stability of membranes in the presence of fluctuating fluid stresses. Most of these problems are of an interdisciplinary nature and call for the collaboration of engineers, physicists, and biological researchers. Fluid dynamicists with a chemical engineering back- ground, in particular, have contributed significantly to the many recent advances summarized below. This has led to the birth of a new field of study, "physicochemical hydrodynamics," in which low-Reynolds- number hydrodynamics and interracial fluid mechanics are inextricably linked with a variety of physicochemical phenomena. The requirements of the chemical and biological applications have necessitated the development of new solution procedures for the treatment of the more complex boundary-value problems that are encountered in these applications. Thus the treatment of small fluid drops near interfaces or droplet coalescence in fluid-fluid separation processes requires a solution technique that can be used to describe not only the fluid motion but also the unknown large-amplitude deforma- tion of the interface and/or the drop due to this motion. The movement of proteins and other molecules in the intercellular channels of biolog- ical cell layers or particle entrance behavior in membranes and nucleopore filters requires the solution of strong hydrodynamic inter- action problems in which the particle motion is greatly influenced by the boundary geometry. In addition, a number of new low-Reynolds-number hydrodynamic phenomena have been either discovered or explained in the recent
FLUID PHYSICS 59 past. It is now realized that there are separated flow regions between particles when the separation is sufficiently small and that this flow separation will have an important effect on the heat- and mass-transfer characteristics of a bed of particles. It is now understood why flexible particles in the absence of inertia will migrate toward the centerline, why a small amount of inertia will cause a particle to migrate to an off-axis equilibrium position, and why finite axial clusters of neutrally buoyant identical particles will break up and form aggregates. The theory for a tiny particle being convected down a tube subject to Brownian motion has led to the development of hydrodynamic chro- matography, a separation classification procedure for identifying par- ticles by size. The sedimentation of particles and dilute colloidal suspensions exhibits several fascinating characteristics that were not previously understood. It has now been shown theoretically why the settling velocities of a fixed array and a random statistical array of particles obey a different power law as a function of density, how orientable particles settle differently than spheres, and how the latter are affected by Brownian motion. The importance of boundaries in the settling process is greatly accelerated in a long slender channel by tilting the channel away from the vertical. The mechanism for this behavior has recently been explained and is currently under study as an industrial separation process. It is evident that much of the growth and progress in low-Reynolds- number hydrodynamics in the past few years is the result of the cross-fertilization that has occurred between researchers in different disciplines as a source of new observations, creative applications, and methods of solution. In most cases low-Reynolds-number hydrody- namics is one essential ingredient of a larger problem. Biological problems, especially at the cellular level, will continue to be a major source of new research primarily because there are so many different cellular functions and unexplained experimental observations. There is still no accepted theory to explain the microstructure of osmosis, the detailed flow and concentration patterns that exist at the opening to pores in biological and synthetic membranes. Electrokinetic phenom- ena will be important both at the exterior surface and within the pore itself. An area that has received relatively little attention because of its complexity is the two-phase convective transport of submicrometer particles that are strongly influenced by Brownian motion. At present much of the work in this area is limited to deterministic motions upon which a weak Brownian motion is superposed. The transition between
60 PLASMAS AND FLUIDS deterministic and statistical behavior is also important in the sedimen- tation of particulates and the study of colloidal suspensions. Thus far the theory of suspensions has only been applied to dilute systems. The effect of electric double layers, particle deformability, and orientation are further topics of considerable current interest in research on colloidal suspensions and emulsions. Progress in many of these prob- lems would be enhanced by closer collaboration between fluid dynamicists and statistical physicists. The recent success in treating droplet and fluid interface problems with large deformations has paved the way for examining a variety of phenomena associated with aerosols and fluid-fluid separation pro- cesses. This research will also be valuable in studying the behavior of surfactant molecules at interfaces, droplet coalescence, deformation of biological cells due to fluid stresses, and related problems. STABILITY Stability of fluid flows is studied, in the first instance, to determine the realizability of proposed flow fields. The main issues historically concerned the onset of thermal convection and the transition to turbulence of shear-dominated flows; more generally the purpose is to predict the possible forms of motion that can branch from a given motion and the sensitivity of these motions to disturbances. In this regard, the subject is now viewed as intrinsically linked to bifurcation theory, the study of the branching processes in nonlinear systems. This broadens the scope of the investigations to inquiries dealing with the forms of "generalized equilibrium states" that arise after the onset of stability. Stability theory, by its very nature, seeks to predict the circum- stances leading to qualitative changes in flow patterns. Consequently, stability theory is a subject of practical technological importance, in that qualitative information concerning industrial processes derived from stability considerations often can be incorporated in design decisions with decisive effects, and the promotion or suppression of fluid-dynamical instabilities is often a crucial technological issue. Motions on geophysical scales, including the dynamo problem, mantle convection, and atmospheric and oceanic current systems, frequently take forms determined by the instability of equilibrium flows arising from fundamental force balances. Useful insights and predic- tions of these forms can be found using stability theory. Consequently, this branch of fluid mechanics figures prominently in oceanography, meteorology, and planetary sciences. It is similarly important in
FLUID PHYSICS 61 astrophysics, in problems concerning stellar convection and galactic structure, as well as in similar questions of considerable interest and importance. Modern advances in this subject have been marked by major changes in conceptual framework as the nonlinear behavior of fluid systems became the focus of an increasing body of work in stability theory, and this has led to much more satisfactory connections between theory and physical experiments. The theoretical advances have been made possible by developments in bifurcation theory, by systematic exploi- tation of multiple-scale and related singular perturbation techniques, by the advent of inexpensive large-scale computation, and by the introduction of increasingly sophisticated experimental techniques. Important new physical effects have been explored, in some cases leading to significant reassessments of phenomena previously misin- terpreted. The effects of surface forces (Marangoni effects) in driving convective instabilities, and effects arising in mixtures (such as double- diffusive instabilities of importance in oceanography, astrophysics, and technological applications) previously treated as single-component fluid systems, have been systematically explored. Magnetohydrody- namic and electrohydrodynamic instabilities, instabilities in liquid crystals, and instabilities induced by complicated indirect effects, such as nonlinear wave-mean-flow interactions, all are examples of new forms of instabilities that were unknown 10 or 15 years ago. Analytical nonlinear theories, originally limited to weakly nonlinear perturbations of a single-instability mode, have been extended to allow for more complicated spatial behavior generated by multiple-mode interactions. Considerable progress has been made along these lines for Benard convection and for Couette flow between rotating cylinders. Extensions of this kind permit information about convection pattern selection to be inferred; this very basic aspect of the motion cannot be obtained from the classical theory. Work dealing with imperfections, that is, slow modulations of motion patterns generated by distant boundaries or nonideal forcing omitted in classical linear theories but having considerable impact on observed patterns of motion, has been appearing. Stability work, including analytical theory, has always required a great deal of computation, and the level of computation has increased with the complexity of the newer problems, particularly perturbation analyses of the kinds mentioned in the previous paragraph. These studies could not have been undertaken without fast computers. Computers have been the essential tools in other modern stability studies. By numerically tracing bifurcating solutions, the restriction of
62 PLASMAS AND FLUIDS weak nonlinearity has been removed, at least in some problems. Thus, the instability of fully nonlinear waves in Poiseuille flow, allowing for some (weak) three-dimensional unstable modes, has been investigated, as have the fully nonlinear instabilities of other flows of classical interest and scientific importance. In addition to these investigations, which deal either with the Navier-Stokes or the Euler equations, computer studies have been made of the evolution of model systems, in which the solutions of the governing equations are represented by a spectral decomposition in spatial variables, and the resulting infinite system of ordinary differential equations (in time) are severely trun- cated. Integrations of the resulting ordinary differential equations, coupled with bifurcation analyses, have revealed bifurcation sequences leading to chaotic motion. In some cases, the results are known to be misleading (for example, the Lorenz equations modeling thermal convection) but seem to be confirmed by integration of the full governing equations in other cases. Thus, the full equations for double diffusion show a period-doubling bifurcation sequence, a well- established route to chaos, and a five-mode truncation model repro- duces this behavior. Large-scale computation, coupled with careful interpretations based on the mathematical framework underlying stability and bifurcation analyses, is likely to yield an extremely rich body of information in the next 10 to 20 years. Almost certainly, the groundwork already laid will produce a much more complete understanding of pattern selection and forms of equilibrated motions deriving from instabilities. Considerable progress can be expected on the problem of the transition to turbulence in shear flows and even greater progress on the transition to turbulence on flows, such as Benard convection, that are destabilized by body forces. It is possible that further links will be forged between the routes to chaos established for systems with a finite number of degrees of freedom and continuous systems. If so, greater insights will be gained about the continuous instability that is fluid-dynamical turbulence. TURBULENCE Turbulence appears in nearly all flowing continua when inertia is dominant relative to the microscopic momentum transport mechanism. It is responsible for most technologically significant drag, heat, and mass transfer and makes life possible on Earth by controlling the distribution of food, heat, moisture, and light in the biosphere. Turbu- lent heat and mass transfer in the magma are probably involved in crustal movement and temperatures. Turbulent heat transfer plays a
FLUID PHYSICS 63 controlling role in the dynamics of stellar atmospheres and of interstel- lar gas clouds and is probably implicated in the gravitational conden- sation of matter from these clouds. The study of turbulence has had as its goal both a philosophical and a quantitative understanding of the physics of turbulent flow, so as to enable numerical predictions to be made in all of these areas. Turbulent transport is usually several orders of magnitude larger than molecular transport, so that when present, it is dominant. Since it is implicated in so many areas of vital concern to humankind, it is clearly important. While the grosser aspects of turbulent behavior are thought to be understood in crude qualitative terms, many of the more subtle aspects are understood poorly or not at all; our ability to make quantitative predictions is extremely limited, and precision is poor. Although turbulence is recognized as the last great unsolved problem of-continuum physics, until recently it was largely-abandoned by mainstream physicists. Developments in the last half-century have been largely due to the engineering community, mathematicians, meteorologists, and oceanographers those who either could not af- ford to ignore the area or were fascinated by it. During this period, vast quantities of data were collected, although not always with imagination. The approach was almost entirely statis- tical. The result was a reasonable grasp of turbulence behavior in many situations and enough understanding of the physics to permit data taken in different circumstances to be placed on a common footing. Several analytical approaches related to techniques used in quantum field theory were applied to the problem; these have resulted more in added insight than useful computational techniques or major theoreti- cal breakthroughs. The advent of large-scale computing has made it possible to solve the Navier-Stokes equations exactly for some simple turbulent flows. This has made accessible quantities that are difficult or impossible to measure but has not replaced experiment; the computations have their own problems relative to the influence of initial conditions on conver- gence and differencing errors, and flows complicated enough to be practically interesting are and will remain for some time beyond economic reach. These exact simulations are limited to relatively low Reynolds numbers; large eddy simulations avoid this limitation by computing large scales exactly and modeling small scales. Otherwise, the large eddy simulations suffer from the same limitation as the exact simulations. Invariant modeling, second-order modeling, and related techniques have been developed to make practical computations. These tech
64 PLASMAS AND FLUIDS niques close the hierarchy of moment equations at various levels (reminiscent of the BBGKY techniques of statistical mechanics). The most interesting of them produce sets of equations for second moments reminiscent of nonlinear diffusion reaction equations or of nonequilibrium thermodynamics of mixtures. Much of this modeling is ad hoc, although it has been possible to base some of it on first principles a posterior). This modeling describes small departures from equilibrium and has corresponding limitations. It has been practically useful, although it has been oversold. More to the point, the construc- tion of the models has been valuable, since it has resulted in much more careful examination of the data and evaluation of the phenomenology and in some cases the taking of interesting new data. The physics community has been particularly stimulated by strange attractors, which explain how some deterministic mechanical systems with three or more degrees of freedom can display apparently chaotic behavior in time and exquisite sensitivity to initial conditions. A number of interesting (in some cases general) properties of such systems have been uncovered. These ideas may explain how turbulent flows can seem to be stochastic, although the extension to continua, and to spatial (as opposed to temporal) complexity, is intuitive. Some light has also been shed on the early transition process. It remains to be seen whether these ideas will help with calculations of fully developed turbulence. Although it has been known for at least 30 years that most turbulent shear flows contained recurrent structures organized on the scale of the flow, little was done with this information. Recent evidence from visualization indicates that these structures are more remarkably coherent than anyone had suspected. The two-dimensional shear layer is not particularly characteristic of other turbulent shear flows, and the relative importance of these structures differs widely from flow to flow. The structures appear to result from instability, either as remnants of the initial instability that formed the flow or as an instability of the fully developed flow, sometimes both in the same flow (as in the wake). There is currently great interest in these structures, their identification, etiology, and prediction, sometimes to the exclusion of the rest of the flow, which remains chaotic. Fortunately, most workers recognize that turbulent flows contain both order and disorder, and techniques are necessary that can encompass, and profit from, both. New statistical techniques are being applied to measurement, nota- bly conditioned sampling to reduce the form of the coherent structures. These can be powerful if carefully used, with proper attention to statistical stability and bias introduced by the condition. These tech
FLUID PHYSICS 65 niques supplement, but do not invalidate, conventional statistical approaches, which often will produce the same statistical information with different accuracy and efficiency. Probably all the approaches currently under investigation will con- tinue so for a while, and others will be added or take their place. We have little faith in breakthroughs in general, and particularly in a field as old as this one; we believe that progress is most likely to come in small increments by increased physical understanding, probably from interaction between careful machine calculations and modeling of various types compared to experiments. Much insight will probably come from investigation of the stability characteristics of turbulent flows and of models and from the inclusion of coherent structures in models. The dynamical systems approach seems very likely to make further contributions, if only to transition. Recent Soviet work relating coherent structures and the dynamical systems approach may bear fruit. The geophysical aspects of turbulence are an interesting special case. The atmosphere and oceans of this and other planets are the greatest natural laboratories for turbulence. There are fully ten decades of scale between the large weather systems and the scale of molecular diffusion. The key problem of geophysical fluid dynamics is first to understand the separate dynamical nature of motions across this range of scales and then to synthesize them into one vast interacting and cascading spectrum. It is not an exaggeration to say that weather prediction, the understanding of the general circulation of the atmo- sphere-ocean system, and the evolving states of climate are all prob- lems of fluid-dynamical turbulence. There are two distinct kinds of geophysical turbulence: small-scale, three-dimensional turbulence and large-scale turbulence whose free- dom is reduced by stratification and planetary rotation. In fact, when the many geophysical constraints like these are added, the turbulence problem becomes intimately related to both wave propagation and flow stability. Of particular interest is the manner in which turbulence and waves interact in systems with buoyancy and rotation. These chaotic mo- tions, in addition, interact with the general circulation of the fluid in a strong manner. A key question under current study is the way in which eddies and the mean circulation mutually influence one another. We are now approaching a clear dynamical understanding of diverse phe- nomena like the Southern Oscillation, stratospheric sudden warming, and quasi-biennial oscillation of the atmosphere and the wind-driven gyres and deep thermodynamically driven circulation of the oceans.
66 PLASMAS AND FLUIDS At smaller scales turbulent mixing of the oceans, in the vertical sense, slowly but persistently determines the gross structure of the temperature, salinity, and trace chemistry. Recent improvements in free-falling instruments have documented this turbulence, but we have yet to describe clearly its bulk effect on the oceans. Studies in atmospheric and oceanic dynamics have, in fact, been the origin of a range of nonlinear physics and mathematics problems, for example, with interactions and Lorenz attractors in systems with few degrees of freedom. BUOYANCY-DRIVEN MOTION Convection in Nature Fluids of nonuniform density are subject to buoyancy forces, under fields of acceleration or gravity. The density variations may originate in compositional differences, suspended particles, phase changes, or temperature variations. The range of phenomena is vast. In meteorol- ogy, cumulus clouds and the global-scale Hadley circulation are examples of convection driven by latent and sensible heat. Evapora- tion and cooling at the sea surface both drives convection that ventilates the depths and, with a time-scale of thousands of years, determines the basic stable density field of the oceans. Where the fluid density is determined by two or more separate components (like salt and heat in the ocean), double-diffusive convection can occur in which rapid diffusion of one component destabilizes the fluid, despite its overall stable density profile. The geological evolution of the Earth's mantle and crust is an instance of convection driven primarily by radioactive heating from below. Fluid models (both theory and laboratory experiments) of these tectonic processes have led to an enormous unification of geology, with practical implications from fossil fuels to earthquakes. At smaller scales the flow and convection of fluids in the presence of crystalliza- tion is beginning to explain the structure of magma chambers, spread- ing centers, and some aspects of volcanism. Turbulent buoyant convection is an especially difficult problem relevant to the transfer of heat, moisture, and momentum in the surface layers of the atmosphere. Turbulence closure theory, and other param- eterization schemes, are being developed to describe the turbulent heat flux and the evolution of the spectrum of velocity.
FLUID PHYSICS 67 Suspended Particles The settling of small particles under gravity through a quiescent liquid is an important physical operation that is used extensively in a large variety of industrial operations. Unfortunately, the process is a very slow one, especially when the particles are small, and hence there exists a need for designing settling devices in which the particle retention times are minutes rather than hours or days. One class of such devices, termed supersettlers, takes advantage of the Boycott effect according to which particles settle a great deal faster where the walls of the settling vessel are inclined rather than vertical. Strong buoyancy-driven convective flows are, however, set up in such in- clined settling vessels that may decrease the efficiency of the process; hence the detailed investigation of these flows is of both academic and practical interest. Gravity Currents The term gravity or density current denotes the flow of one fluid within another, caused by the density difference between them. The fluids are usually miscible, and the mixing that results can play an important part in the dynamics of the flow. Gravity currents are encountered in situations of geophysical and atmospheric interest and have important applications to aircraft safety, atmospheric pollution, or industrial accidents involving the spread of a dense gas such as liquefied natural gas from an accidental release. Convection in Materials Processes Temperature- and concentration-induced buoyancy-driven flows oc- cur frequently in materials-processing operations such as crystal growing, with both desirable and undesirable consequences. Convec- tion of course increases the overall transport rate of heat and mass and hence the growth rate; on the other hand, the morphology of the solid is usually affected adversely. INTERFACE PHENOMENA Flows with interfaces between two or more fluids occur frequently in nature and play an important role in a wide variety of physical phenomena. All of these share the common feature that the domain of interest involves a boundary of unknown shape whose evolution,
68 PLASMAS AND FLUIDS generally in time, is one of the primary goals of any theoretical or experimental investigation on the subject. The problem of determining this interface often requires novel experimental, analytical, or compu- tational tools. We list below some of the more important topics that are being actively investigated at present. Deformation and Breakup of Small Drops in Shear Flows In many industrial processes it is often required to disperse one liquid phase into another with which it is immiscible. One wishes then to design an appropriate mixing device and to determine the power necessary to ensure that the size of the largest drop comprising the dispersed phase does not exceed a given value. Breaking of Waves When designing harbors and coastal breakers, one wishes to deter- mine the shape of the waves as they advance onto the beach, find out where they break, and then calculate the energy that is released. In view of their potential for causing great damage, the behavior of tsunamis is particularly relevant in this connection. Sediment Transport This involves the modeling of ripples and dunes as well as the study of coastal sediment processes. The transportation of solid-liquid sus- pensions, such as slurries, in pipelines and the determination of the many possible flow regimes that can occur are also topics of consid- erable current practical interest in this area. Solitons Solitary waves, on the surface of shallow layers as well as in layers of infinite depth containing regions of nonuniform density, are cur- rently being studied extensively because of their remarkable property of being able to propagate without change of shape and to maintain their identity on colliding either with a stationary object or with another such wave. Solitons play a central role in many phenomena of geophysical significance.
FLUID PHYSICS 69 Spreading of Liquids on Solid Surfaces This topic is of considerable theoretical interest because it involves the motion of the contact line, i.e., the intersection between two immiscible fluids and a solid surface. Clearly, this motion, which is certainly observed experimentally, violates the universally accepted no-slip boundary condition, which must therefore be replaced by something more complicated. Coating flows, which are of great impor- tance in the photographic industry, also involve the motion of contact lines. Air-Sea Interaction The atmosphere and oceans form an interlinked system. The trans- port of gases, heat, moisture, particulate material, and momentum across the air-sea interface is a phenomenon relating to the evolution of climate, weather prediction, and the distribution of trace chemicals and man-generated pollutants. On both sides of this interface lie turbulent boundary layers. The interface itself is a convoluted surface, with breaking surface waves that inject bubble clouds into the sea below. Recent advances in observational oceanography and boundary-layer meteorology are leading to qualitative improvement in our understand- ing of the small-scale mechanism. For problems of global scale, we are coming to rely on remote sensing, particularly from orbiting satellites, to provide air-sea transfer maps. SOUND GENERATION AND PROPAGATION Generally the field of acoustics is well understood provided we stay out of the nonlinear range. The transition from linear acoustics to nonlinear acoustics and the interaction of acoustic phenomena with flow fields are just beginning to be understood. One of the items mentioned earlier in the section on High-Speed Flows the control of turbulence-will also play a fundamental role in the control of the generation of sound by jet aircraft. It is generally the turbulence of the jet that creates the largest portion of the sound field, and this control will allow a further reduction of the perceived noise of jet aircraft. The radiated acoustic energy of jet aircraft was reduced nearly 1000-fold during the 1970s, mainly by reductions of jet velocity, which yielded the collateral benefit of much improved propulsion efficiency. Another factor of this magnitude could be available if we can control the jet mixing process. As the noise from the inlet and jet exhaust become
70 PLASMAS AND FLUIDS suppressed, the next dominant noise will be due to the turbulence on the wings and fuselage. The process for controlling the turbulence of the aircraft is important not only to the reduction of drag of the aircraft but also to the reduction of the internal noise of the aircraft. The transition from linear to nonlinear acoustics is important in several fields of technological interest, including the fracture of rocks by high-speed water jets. We still do not know the fundamental physics of the focusing of acoustic waves to form caustics and cusps in caustics. The unsteady body forces that occur principally in helicopter rotors, engine compressors, and propellers are also important generators of noise. Basic understanding of the mechanism of noise generation, and the application of this understanding to problems such as the interac- tion of a helicopter rotor blade with the previous blade's trailing vortex, has led to considerably quieter aircraft and helicopters. The acoustic analogy that provided the insight needed to greatly reduce jet noise is now aided and abetted by the understanding being provided by the application of rapid distortion theory. This theory linearizes about a mean steady flow and assumes that the characteristic time for the interaction of this flow with its unsteady variations is short compared with the characteristic time for the decay of this unsteadi- ness. The application of these ideas accounts for sources of acoustic radiation beyond those recognized in the original acoustic analogy. RADIATION HYDRODYNAMICS One particular subfield of fluid dynamics that is both intellectually challenging and of great importance is radiation hydrodynamics, which also goes by the names radiation-coupled flows and radiation-induced flows. This is basically the study of hydrodynamic phenomena at very high temperatures, in which the thermal radiation field associated with matter affects the dynamics of the fluid. The importance of thermal radiation in fluids problems increases as the temperature is raised, primarily because the radiation energy density associated with a Planck distribution varies as the fourth power of the temperature. At low temperatures (say, room temperature) radiation effects can generally be completely ignored in the fluid flow context. One important excep- tion is the radiatively driven flow in some planetary atmospheres. At moderate temperatures (say, thousands of degrees) the role of radiation is primarily one of transporting energy by radiative processes. At higher temperatures (say, millions of degrees) the energy density and pressure associated with the radiation field can become comparable to
FLUID PHYSICS 71 or even dominate the corresponding fluid quantities. In this case, the radiation field significantly affects the dynamics of the field. Fluid flow with explicit account of the radiation energy and momentum contribu- tions constitutes the character of radiation hydrodynamics. The rele- vant fluid equations, namely, the energy and momentum balances, contain additional terms accounting for these radiative contributions. These terms in turn are computed from an auxiliary equation, the equation of radiative transfer, which is a kinetic equation describing the flow of photons in phase space. Thus radiation hydrodynamics involves the simultaneous solution of the fluid equations and a kinetic equation. Because of the high temperatures involved, viscous effects can generally be ignored, and often heat conduction can be ignored as well. In addition to the inherently rich physical and mathematical content of these equations, the study of radiation hydrodynamics is of great practical importance. It is clear that applications of this field will involve physical phenomena at very high temperatures. The primary applications involve three areas of great import to mankind. The first is found in astrophysics, where the underlying purpose is to obtain a better understanding of our universe. The second involves national defense. A thorough understanding of radiation hydrodynamics is essential for predicting nuclear-weapons behavior and effects. The third significant application of this field is found in the energy arena. Any calculation of inertially confined fusion concepts, be it laser- or particle-beam-driven, must be based in large part on the equations of radiation hydrodynamics. Because of the complexity of the radiation hydrodynamics equa- tions, very few meaningful analytical solutions can be found. Thus the challenge has been, and continues to be, the development of accurate general-purpose numerical methods for solving the coupled set con- sisting of the fluid equations with radiation terms and the equation of transfer. To date, both Eulerian and Lagrangian formulations have been developed, in one- and two-dimensional generality. However, the corresponding treatment of the radiation field has been limited to diffusion (moment) approximations to the equation of transfer, as well as the generally prohibitively expensive Monte Carlo method. It is becoming increasingly clear that the diffusion approximation is simply not accurate enough to describe certain physical phenomena ade- quately. Thus what is required on the near to medium future time scale is the development of Eulerian and Lagrangian methods for fluid flow, coupled with more accurate (than diffusion theory) and less expensive (than Monte Carlo) solution methods of the equation of transfer.
72 PLASMAS AND FLUIDS Ideally, one would like a three-dimensional capability, but it is more realistic for now to think in terms of one and two dimensions. Such methods should be unconditionally stable as regards the time differencing of the equation of transfer, must be capable of producing numerical results with a vanishingly small truncation error in the limit of small cells, and must give a qualitatively correct result (the diffusion limit) for large cells. In this regard, it is recognized that both parallel processing and vector computers are on the horizon, and research is needed as to how the equations of radiation hydrodynamics, in their numerical form, can best be structured to take advantage of these advances in computing technology. A final area of need relevant to this subfield of fluid dynamics concerns the basic data problem. Because of the high temperatures and pressures inherent in radiation hydrodynamics prob- lems, very little relevant equation-of-state and opacity data can be obtained in the laboratory. Thus, continued development is required to improve our theoretical models and calculational techniques for these basic data. Included in this is the increasingly important need for local thermodynamic equilibrium (non-LTE) calculational methods, in which opacities are based on the solution of rate equations describing the population levels of the various states of the atom, rather than on a simple thermodynamic formulation. Given the proper support and environment, many important ad- vances can be made in the coming years to enhance our understanding and calculational ability of radiation hydrodynamic phenomena. This will be an intellectually stimulating development process, cutting across many disciplines and yielding results that have practical signif- icance in several important national endeavors. POROUS MEDIA With the current interest in oil exploration, the various phenomena that are associated with the flow of matter and energy through porous media are receiving an increasing amount of attention from the fluid-mechanics community. In general, single-phase flows can be described by Darcy's law, according to which the velocity is proportional to the pressure gradi- ent. The magnitude of the coefficient of proportionality is, however, unknown as is its dependence on the various properties of the porous material, for example, the void fraction, the tortuosity of the inter- stices, and the particle size distribution. Several attempts have there
FLUID PHYSICS 73 fore been made to develop a theory for estimating the permeability, and recent results using percolation theory appear promising. In the case of single-phase porous media flows in soil mechanics and soil hydraulics, additional complications arise that require that the permeability be assumed anisotropic as well as a nonlinear function of porosity and pressure. Environmental problems include wind, water and sea erosion, the permeation of soil by seawater, and land recla- mation through irrigation. Important biological porous media flows include the interstitial fluid flow in the articular cartilage, the drainage of intraocular fluid in the eye, blood perfusion in living tissue, and other applications that are mentioned in the section on Biofluid Dynamics. From a practical point of view, however, the subject of multiphase flow through porous media is an even more important one, especially as concerns oil exploration, but here a reliable theoretical framework (i.e., an extension to multiphase flow of Darcy's law) for modeling the various phenomena is lacking. For example, little is known quantita- tively about the dynamics of oil ganglia during immiscible displacement in water-wet porous media, and many fundamental questions that are associated with secondary and tertiary oil recovery remain very much unanswered. The very complicated simulation models that are cur- rently being used in industry are therefore based on a very incomplete knowledge of the physics underlying the various processes. ROTATING PHENOMENA In this class we place those flows in which Coriolis forces and radial accelerations due to large-scale rotation introduce phenomena not present in flows naturally referable to inertial coordinates. Turbomachinery Flows Strong rotation is an essential feature of turbomachinery flows, as it is necessary to the angular momentum exchange that provides the energy transfer in these ubiquitous devices. The resulting radial pressure gradients and Coriolis forces play essential roles in the behavior of the viscous three-dimensional flows that limit the energy exchange and efficiency. Owing to their great complexity these phe- nomena have been understood only superficially. With rapidly evolving computational and experimental capabilities, however, these flows will soon become tractable, giving us the possibility of much more rational and effective designs. The potential for energy savings is enormous.
74 PLASMAS AND FLUIDS The Circulation of the Atmosphere and Oceans Motions of the atmosphere and oceans at scales greater than a few kilometers, and time scales greater than a day, feel the Earth's rotation strongly. The Coriolis force and pressure gradient are the dominant forces in both ocean currents and weather systems. Modern comput- ers, theory, and modern field observations are combining to give us, for the first time, a complete dynamical picture of these circulations. Planetary rotation puts severe constraints on the flow, for example, limiting the heat flux from equator to poles and shaping the great wind-driven gyres that fill the upper kilometer of the oceans. The problems of climate change and weather prediction, pollution, and the chemical evolution of Earth and the planets all involve the dynamics of rapidly rotating fields. With planetary rotation, small-scale fronts and turbulent boundary layers provide a particular challenge, both as fundamental nonlinear dynamics problems and as bottlenecks to the understanding of the large-scale flows. Coriolis forces give weather systems their distinctive nature, which involves elements of Rossby wave propagation, insta- bility, and geostrophic turbulence. The determination of the general circulation of oceans and atmospheres rests on theory and observation of these energetic elements, and the calculation of their back interac- tion on the mean flow. PHASE CHANGE Phase change is an important element of both natural and industrial processes. Technological Applications Phase change between liquid and solid states is important to a range of practical problems, for example, energy storage devices, shipment of natural gas and oil through pipelines in cold latitudes, cryosurgical problems like the freezing of living tissue with blood perfusion, storage of blood with cryopreservation, metal cutting and dendrite formation, crystallization, and plating phenomena. Classical fluid-mechanics techniques like stability theory are being applied, for example, instability theory to model the formation of dendrites in a supersaturated salt solution. The geometric aspects of these problems are often complex, but the range of valuable applica- tions is large. Phase change with irregular boundaries is being modeled
FLUID PHYSICS 75 for the case of metal castings. In the complementary case of laser metal cutting, the problem is to model melting around a moving heat source. In the case of phase-change energy storage devices, one is faced with a difficult free-convection problem in complex geometry. Cryosurgery as a modality in the treatment of tumors has received considerable attention in the past decade as has the cryopreservation of blood and other living tissue. This freezing is complicated by the nonuniform vascular geometry and regional blood flow in living tissue and solute concentration effects at the cellular level. Pipe flows may experience phase change if cooled from the exterior; viscous heat generation begins to compete with exterior cooling once the aperture has been reduced. If the pipe is embedded in frozen tundra, the prediction of the melting and ice front in the exterior region must be carried out in parallel. Nonequilibrium Evaporation and Condensation Nonequilibrium condensation and evaporation phenomena have long been of interest in high-speed fluid mechanics. The fluid mechan- ics of strongly vaporizing or condensing surfaces and the nonequili- brium statistical mechanics of the homogeneous formation of clusters of "multimers" have been studied in the last decade. Both phenomena have numerous potential applications in a variety of industrial pro- cesses and in understanding natural events. In the coming decade it is expected that investigations of cluster formation, and more generally nucleation in supersaturated vapor flow, will provide insights into these important problems, which are at present not well understood. These studies appear to be most success- ful when done in gas-flow situations, where it is relatively easy to obtain arbitrary degrees of supersaturation. For example, recent results on the probability of occurrence of numbers of molecules in a cluster provide an indication of the cluster's topology or packing scheme. Heterogeneous nucleation phenomena are also extremely important and difficult to describe. It is to be expected that research on homogeneous nucleation will lead to a better understanding of the heterogeneous problems. A related subject is bubble formation, both heterogeneous and homogeneous, which enters into many practical situations. Boiling heat transfer and cavitation are two examples. This area presents a wide range of problems that will continue to be of interest.
76 PLASMAS AND FLUIDS Geophysical Flows Changes of phase of water are at the heart of weather-and climate dynamics. Evaporation at the sea surface and recondensation in tropical cumulus clouds provide the principal motive force for the atmospheric circulation. The evaporation stage involves complex dependence on humidity, wind, and sea state. The process is embed- ded in turbulent boundary layers both above and below the sea surface. The condensation of water vapor into clouds requires condensation nuclei, and there is a complex of surface chemistry and particle kinetics that interacts with the fluid dynamics of the convecting cloud. Beyond the dramatic examples of these heat engines, like hurricanes, the dynamics of tropical cloud clusters is a central problem in atmospheric dynamics. Parameterization of cloudiness and precipitation in numer- ical models of the circulation is a significant unsolved problem. Successful three-dimensional simulations of rudimentary, individual convecting clouds are now being carried out; they require the fastest available vector computers. Sea-ice and terrestrial ice and snow cover affect the dynamics of climate most directly. Floating ice is a complex material, and its growth, movement under wind stress, and fracture are difficult to predict. Freezing produces heavy, saline water, which is a primary cause of deep convection in the high-latitude seas. Once developed sea ice insulates the ocean from further heat or moisture flux. Large-scale models of ice dynamics are beginning to reproduce these effects, while small-scale experiments and observations have clarified the process by which seawater freezes and drains itself of brine. On land, the hydrologic cycle is a fluid-dynamical problem involving phase change and flow through a complex porous medium. As with the ocean, the groundwater and snow cover act as a memory for climate evolution and long-range weather predictions. Topical Subject Areas AERODYNAMICS New theoretical understanding through asymptotic methods, the addition of numerical simulation to theory as an investigative method- ology, the use of computers in data acquisition and analysis, and a better understanding of the physics of turbulent processes has accel- erated the pace of accomplishment in aerodynamics. Inspired by these intellectual advances as well as by pressing needs, significant contri
FLUID PHYSICS 77 buttons have been made to the efficiency of commercial air transports, the performance of helicopters, manned re-entry vehicles, and the effectiveness of military aircraft and weapons systems. One of the principal ingredients to these advances has been the use of the computer as a numerical simulator to aid and abet the understanding of high-speed flows, to assist in data analysis, and as a design tool. Another has been the extension of asymptotic analyses to provide an understanding of the rich physics of flows, such as those about a wing's trailing edge that sets its circulation and determines its lift. A third ingredient has also been realized and has already seen application in flows such as those about helicopter rotor blades. Important recent advances include the development of efficient aerodynamic algorithms for simulating the flow about aircraft, detailed understanding of how viscous and inviscid flows interact, the aerodynamics of supercritical flows, and the utilization of shock-free flows once deemed physically unrealizable. There are manifold opportunities for major advances in high-speed flows that will extend the developments of the past decade. These past developments have been focused in three primary technological areas: the development of highly efficient commercial and military transports, the development of highly maneuverable fighter aircraft, and the turbomachinery of aircraft engines. These developments will continue primarily from advances in our understanding of separated and un- steady flows, from our special knowledge of new aerodynamic design procedures, from our beginning understanding of and thereby our ability to model and perhaps control, turbulence, and from the con- tinuing growth in the use of computers to simulate aerodynamic flow fields. In many flows of technological interest the flow is either separated or unsteady or both. We are beginning to understand the fundamental physics of these separated and unsteady flows and how, often in combination, they can be used to improve the efficiency and performance of technological devices. It has been known for some time that the aerodynamic designs that operate at high subsonic Mach numbers are most efficient if they can avoid the generation of shock waves. But such flows are isolated from one another and were originally thought to be impractical. It has been demonstrated over the last decade that these mathematically isolated solutions are of practical value, and special techniques have been developed to find them. These techniques have now been generalized to the point where they can be used routinely in the design process guaranteeing that the extremes of the transonic design envelope can be reached.
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80 PLASMAS AND FL UlDS By the end of the century we may achieve another doubling of the fuel economy of the present-day transport aircraft. This doubling will occur through a number of design innovations in the aerodynamics of high-speed Hows, both external to the craft and through its engines. Aerodynamics will contribute significantly to this improvement. For this reason alone, the fundamental physics of these flows is especially important. In addition, there are many devices whose designs may be altered radically if one turns from steady attached flows to unsteady separated flows to improve their performance. Our understanding of the physics of these unsteady separated flows is just beginning and is especially important. It is clear that in some areas the Europeans are catching up with us in the application of fundamental advances in computational fluid dynamics (CFD) and turbulence. Some believe that they will soon achieve parity in distinguishing real physics from numerical physics, and that they are more rapidly capitalizing on the availability of supercomputers than we are. On the other hand, it is clear that the Soviet Union, while relatively strong in theory, is weak in CFD. While many European facilities are newer and better than ours, generally these facilities derive from ideas that were first implemented in the United States. The principal bottlenecks to rapid progress in aerodynamics are the inadequate university access to supercomputers, current limitations in computer CPU size, the inadequate funding of university research, the obsolescence and cost of some of our experimental facilities, and the lack of an understanding of transition and turbulence. Research funding needs to address all three elements of the trilogy that com- prises analysis (theory), experiment, and numerical simulation. Table 2.3 delineates past, but still recent, advances, their technolog- ical applications, areas of rapid advance and opportunities, the imped- iments to progress in some of these areas, and the status of foreign competition where appropriate. We are now beginning to understand better the fundamental physics of the process of transition to turbulence, and through that understand- ing we are beginning to develop methods to suppress this transition and even turbulence. These controls range all the way from acoustic input to the boundary layer through the removal of a substantial portion of boundary layer from the surface. . .
Ff UlD PHYSICS 81 BIOFLUID DYNAMICS In the past decade, biofluid-dynamics research has undergone an unparalleled growth that has touched on our understanding of nearly every aspect of human, animal, and plant function where fluid- mechanical flows and forces play a significant role. A very positive climate for interdisciplinary research and mutual dependence and acceptance has evolved since the late 1960s between researchers in the biological and medical sciences on the one hand and the physical sciences and engineering on the other. We shall briefly summarize here a few major areas of activity where either significant advances have been made in the recent past or a major development of new ideas is in progress. What earmarks all of these problem areas is that the mathematical models or laboratory model experiments constructed to explain the phenomena are much more closely linked to biological reality than in the past because of close collaborations that have gradually developed with biological and medical researchers. The study of the flight of birds and insects, the swimming of fish and mammals, and the locomotion of microorganisms has been a constantly expanding interest of fluid mechanicians over the last half century. In the past 10 years, new insights have been obtained into the flight formations of birds, the wave skimming of seabirds, the hovering aerodynamics of bees and hummingbirds, the efficient swimming of large fish such as the tuna, and the flagellar and ciliated propulsion of numerous microorganisms from the cholera-causing bacteria Vibrio comma to the mucociliary motion of an egg cell in an oviduct. Theory and elegant validating experiments have been performed to explain the progressive metachronal wave motion of cilia and the mechanism of mucociliary pumping that are vital in the reproductive organs and the bronchial and tracheal air passages. Most recent studies suggest that the Theological properties of mucous may have a profound effect on the swimming of sperm and that more basic studies of the microstructure of this fluid are needed. The effect of thermally induced motions on the swimming of mammals and large fish is another new area of consider- able interest. A problem area that has attracted widespread interest in the past decade is the fluid-dynamic aspects of arterial disease. There is a growing body of evidence that strongly suggests that the small popu- lation of endothelial cells (inner cellular lining of blood vessels) involved in turnover (cell death and replacement) at any given time can produce large changes in the permeability properties of the artery wall to lipoproteins and that these changes induced by fluid shearing
82 PLASMAS AND FL UlDS stresses may be an important initiating factor in arterial disease. Experiments have been conducted and a microhydrodynamic theory proposed to understand the vesicular transport of cholesterol and other large molecules across the endothelial lining and the effect of fluid stresses on endothelial cell function both in tissue culture and in viva. Sophisticated numerical and laboratory models of the larger vessels have been constructed to ascertain the stress distribution in viva, and these models have been correlated with the known predilection sites for atheromatous lesions observed in animal experiments and autopsy. Cardiovascular fluid mechanics and the theological properties of flowing blood have been a traditional area of study for biofluid mechanicians. Much of the previous research in this area examined the arterial tree as a branching, nonuniform transmission line for the propagation and attenuation of the pulse pressure or studied the non-Newtonian flow properties of blood. In the past decade, new avenues of research have been initiated on the fluid mechanics of the highly compliant and collapsible veins, on the motion of the deformable cellular components of blood in the microcirculation, and on a more realistic numerical modeling of the ventricular action of the heart. Several new phenomena have been discovered in the nonlinear re- sponse of a collapsible tube under steady and unsteady flow conditions as a model for certain flow phenomena in the venous and bronchial trees. Similarly, intriguing new behavior such as the tank treading of a red cell membrane in a shear flow have been observed and explained in microcirculatory flows. Other microcirculatory flow phenomena, e.g., the hematocrit defect in an entire capillary bed, still have no satisfac- tory explanation. There are a number of important phenomena in which biological tissue behaves as a porous medium. Prominent examples include the movement of interstitial water and solute diffusion in loaded articular cartilage, the filtration of blood plasma across the walls of the blood vessels, the drainage of interstitial fluid in the lymphatic circulation, the hydration of the cornea, and the drainage of aqueous humor from the anterior chamber of the eye. In all of these problems one is examining the consolidation of a biological porous matrix under pressure loading coupled with biochemical-physical phenomena. A different type of two-phase flow problem is encountered in bioheat transfer theory. Here one would like to determine how the local heat-transfer characteristics of tissue are affected by the blood flow. An especially fertile area for future research is cellular and microhydrodynamic transport processes. These problems are fre- quently complicated by the presence of electrostatic, electrodynamics,
Ff UID PHYSICS 83 and chemical forces. Linear stability theory has been applied to the cell membrane modeled as a viscous fluid layer subject to a perturbation in molecular forces at its surface. Important cellular transport processes currently under study and of great interest to cell biologists are endocytosis, exocytosis, and vesicular transport. The movement of molecules at the entrance to and their passage through the intercellular channels between adjacent cells in a cell layer provides the hydrody- namic basis for both the microstructure of osmosis and the phenome- nological coefficients universally used by the biological scientists in describing their membrane transport experiments. The transport of water, small ions, and proteins occurs at discrete locations in a cell layer and not uniformly across the entire membrane surface, as is the case for gaseous molecules. The consequences of this behavior for the transport in the underlying tissue are just starting to be explored. In the lung the flows of gas, blood, and water are of equal impor- tance, and they take place in an organ that is very flexible. The blood vessels and the alveoli go through large deformations in normal lung function. The oxygenation of blood and removal of CO2 relies on the participation of a number of enzymes, which greatly facilitates the mass transport. The flow of water into the lymph or alveoli determines whether one has edema or not. The structural basis (ultrastructure, molecular biology) of the capillary blood vessel wall determines the health or disease of the blood. Thus, in order to understand ventilation and perfusion, fluid dynamics has to be coupled with nonlinear finite elasticity and biochemistry. There has been significant progress made in the past decade, but a detailed quantitative understanding awaits the future. This brief summary has omitted many fascinating problems involving specialized organs such as the eye, ear, urinary and gastrointestinal systems, and the placenta, where there continue to be many research opportunities for the fluid mechanician. We have also focused on basic physiological processes and have not mentioned the wide range of new medical devices, instruments, or prostheses that have been introduced or the major advances that have been made in the design of artificial organs through the application of fluid-dynamic principles. The search for new noninvasive techniques for measuring local blood How for clinical diagnosis continues. FLOWS OF ELECTRICALLY CONDUCTING FLUIDS By interaction with magnetic fields, either self-induced or imposed, electrical conductivity introduces body forces and energy coupling to
84 PLASMAS AND FLUIDS the bulk fluid, resulting in a complex of phenomena not present in the classical fluids described by the Navier-Stokes equations. These range from pure magnetohydrodynamic phenomena such as Alfven waves and forward propagation of viscous wakes to the more complex category involving thermal and ionization phenomena, such as the ionization or electrothermal instabilities in nonequilibrium plasmas. Studies of these complex phenomena have provided explanations for the behavior of the Earth's core, for events in the Sun's corona. The continued study of magnetohydrodynamics is essential to future progress in these areas, and in cosmology. Potential engineering applications of magnetohydrodynamics (MHD) include fusion power, electric circuit breakers, electric space propulsion devices, manipulation of molten metals, and MHD power generation. Fusion is addressed at length elsewhere in this report. After a very intensive effort over the last 20 years, funding for electric propulsion and MHD power generation is currently at a low level. Yet many important phenomena remain partially explored or perhaps undiscovered. It is important to continue fundamental work in this area, which, quite apart from its intellectual challenge, may have additional important applications in the future. GEOPHYSICAL FLUID DYNAMICS The fluid dynamics of the natural world encompasses a vast range of physical phenomena, from atmospheric and oceanic dynamics and climate change to geological processes in the Earth's mantle and core. The subject has evolved naturally to consider the atmospheres of the planets and fluid phenomena in astrophysics. What makes the geophysical fluid dynamics (GFD) of the atmo- sphere and oceans challenging is the ten decades of scale between the motions of planetary scale and the motions of smallest scale, where molecular diffusion is important. Thus a theory or computer simulation of the weather must somehow incorporate the cumulative effect of all the smaller-scale fluid dynamics: internal waves, fronts, two- and three-dimensional turbulence, and convective clouds. Intense studies of these intermediate scales of motion are being pursued, for example, with much progress on severe storms, cloud modeling, and frontal dynamics being evident. A simulation of climatic change must in addition accurately account for the many years of weather, whatever its cumulative effect may be. A theory of the ocean circulation, on the other hand, must cope with its vastly slower response to a change in atmospheric winds or heating. It
FLUID PHYSICS 85 must account also for the differing behavior of salinity and tempera- ture, both of which influence the fluid buoyancy. At high latitude the dynamics is made complex by sea ice. The oceans act as a flywheel in the climate system with a time scale as great as a thousand years. The worldwide disruption of weather by the 1982-1983 El Nino event in the tropical Pacific Ocean shows us the powerfully interactive nature of the oceans and atmosphere. Wave-propagation theories have successfully described several of the links in the sequence of tropical and global change. Beyond these short-term events we are soon to experience the global effect of increasing carbon dioxide in the atmosphere. The prediction of climate change over the next half-century relies on complex fluid- dynamical modeling of the general circulation and its heat and moisture balances. These important problems involve, in addition to classical fluid dynamics, interactions with chemistry (for example, of aerosols in the atmosphere and carbon in the oceans), radiative effects, multiphase and multicomponent fluids (as in convective clouds and in sea ice), and biology. (The biosphere interacts with the fluid atmosphere and oceans in many ways.) Such interactions are crucially important in the possible aftermath of nuclear war, in which the particulate load of the atmosphere may be great and the Sun obscured for months or years. A promising branch of study in this area is Lagrangian fluid dynam- ics, in which theory and measurements are carried out using the moving fluid particles as a reference. We are seeing rapid progress in the understanding of the oceanic general circulation, both the mechanical response to the stress exerted by the winds overhead and the thermodynamical response to heat flux and moisture flux between the air and sea. The complexity of the system would defy any brute-force solution by computer simulation, but there is much optimism that new techniques will lead to a solution: first, radically new measurements of the atmosphere and oceans are now possible using microelectronics, remote sensing (especially from orbiting satellites), and computer analysis, and, second, simple theo- retical models of the circulation are emerging that help to reduce the apparent complexity of the system. These theories of the circulations, wave propagation, turbulent cascades, and the induction of mean circulation by eddy motions are laying the groundwork for the coupled model of the ocean-atmosphere system. The close interaction of theory, observation, and computer and laboratory experiment are characteristic of the work. The study of the atmosphere of other planets has a close connection with GFD: while many new physical and chemical ejects are present
86 PLASMAS AND Ff UlDS on the planets, some remarkable tentative similarities have been found with terrestrial flows. Beyond their own intrinsic interest, the value of studying the other planets is to better understand our own. Intense, isolated vortices, for example, have been observed in Jupiter's circu- lation; models of them have aided in understanding terrestrial flow, from small severe storms to the intense eddies cast off from the Gulf Stream. Terrestrial general circulation models have been able to simulate some of the banded flows of the outer planets, simply by altering appropriately their planetary rotation and density stratifica- tion. MULTIPHASE FLOWS The analysis of flows in which more than one phase is involved (multiphase flows) offers problems of far more complexity than are encountered with single-phase flows. The reason for this is that the different phases, in general, are not uniformly mixed, and a detailed understanding of how these phases are distributed in a flow field is needed. The importance of these flows can be realized by considering a few examples: · The transport of crude oil in a pipe usually involves the flow of both liquid and gaseous hydrocarbons. In horizontal pipes at low gas and liquid velocities a stratified configuration is attained whereby the liquid flows along the bottom of the pipe and the gas concurrently with it. Increases in the liquid velocity or a change of orientation to an upward inclination can give rise to a situation where the gas and liquid flow intermittently, thereby creating large pressure pulses, which in turn can cause vibrational damage. Thus, it is usually desirable to design so as to avoid slugging, but, unfortunately, currently available scaling laws are unable to predict either the conditions under which slugs will appear or their properties. · Another example is found in nuclear reactors, which typically employ water to remove the heat generated by the nuclear decay. A two-phase flow of vapor and liquid occurs in the cooling passages because of the boiling of the liquid. The flow character can vary from a bubbly flow, which consists of a mixture of vapor bubbles and liquid, to an annular flow, whereby a mixture of vapor and liquid droplets flow concurrently with a liquid film on the wall. It is critically important to design these cooling systems so that the wall film does not dry out, because under these circumstances the cooling is insufficient and a runaway reaction can occur.
FLUID PHYSICS 87 · As a final example, we mention the transportation of solids, such as coal, in a slurry in a pipeline. Here one of the chief engineering considerations is to avoid settling of the particles, which is accom- plished by selecting a proper size range for the particles and a judicious pipeline design. In a long straight pipeline the particles settle because of gravitational forces; this is opposed by turbulence and other hydrodynamic effects, in a manner that is not yet understood. Further basic research on these hydrodynamic effects is needed to provide a solid theoretical basis for the design of slurry pipelines. In fact, it is not an exaggeration to claim that almost every aspect of a manufacturing facility in the chemical process industry is confronted with multiphase problems. This can involve the contacting of gases and liquids or of solids and liquids, the design of condensers and boilers, the evolution of gas in a chemical reaction, the design of pressure relief valves, or the separation of phases. Quite often the failure of a process design (usually at great cost) can be traced to a poor understanding of the consequences of a scaleup of some part of the system involving a multiphase flow. The recognition of this problem has led large compa- nies to identify critical parts of the flow system and to do full-scale tests to ensure a safe process design. The problem of scaling multiphase problems can be illustrated by considering the prediction of pressure drop in a long straight pipe. Here, in contrast to single-phase Hows where reliable correlations exist that do not require detailed knowledge of the turbulent flow field, in multiphase flows there are so many independent variables defining the system that dimensional analysis leads to too many dimensionless groups to be of use. Consequently, in multiphase flows one has to have a detailed model of the physics of flow in order to correlate test results in a meaningful way. Current design methods, given in engineering handbooks, usually involve the modification of single-phase relations by using fluid prop- erties that are some combination of the properties of the different phases, an approach the inadequacy of which has been recognized for 25 years. It is quite clear that predictive methods for pressure drop must be tailored to the flow configuration that is expected to exist. Research in this area has three main aspects: (1) basic studies of multiphase phenomena, (2) the prediction of how the phases distribute for different flows, and (3) the development of design equations as well as computer codes for predicting the distribution of phases in complex flow situations. Basic studies would involve such issues as the mech- anism by which particles are entrained and moved by turbulence in a
88 PLASMAS AND FL UlDS flowing gas stream or the mechanism by which waves are generated by air flowing over a liquid film. The second aspect of this research involves the use of diagnostic tools to determine how the phases distribute in a particular flow and the use of basic studies to provide an explanation of the observed distribution. The final aspect of research on multiphase flows is the development of design equations and computer codes to predict phase distribution. To date, it has become customary to consider separate differential equations for each phase and to use these as the basis for the computations. Unfortunately, it is quite likely that this aspect of research on multiphase flows is danger- ously ahead of our basic knowledge. Technical Disciplines MODELING AND ANALYTICAL METHODS Phenomena found in the natural world and in the industrial environ- ment are identified and described in physical terms. This physical description must then be expressed mathematically in nondimensional form. This delineates the dominant physical mechanisms. These equa- tions are then solved by asymptotic or analytical methods or by numerical means. This process includes the development of physically viable conceptual models based on a synthesis of available data, the generation of rationally derived governing equations and the corre- sponding and initial boundary conditions, and the development of solutions to quantify the physical process of interest. All Newtonian fluid-physics processes are described ultimately by a suitably generalized set of Navier-Stokes equations in which chemical effects and radiative transfer may be included. Suitable analogs are developed for non-Newtonian fluids. Unless the solution process is to be based on numerical simulation of the complete general equations, rational approximation schemes are needed to reduce the full mathe- matical system to a simpler form compatible with the physical model. Significant parameter groups are identified and then employed to develop asymptotic representations of the complete equations. Meth- ods of this genre have permitted an enormous improvement in the understanding of classical ad hoc approximations (for example, bound- ary-layer theory and potential flow theory) and facilitated the develop- ment of techniques for describing very complex flows including, for example, multiple-deck descriptions of trailing-edge flows, shock/ boundary-layer interactions, and delta-wing aerodynamics. In fact, major processes in every branch described in this chapter, with the
FLUID PHYSICS 89 notable exception of turbulence phenomena, can be attributed to the use of contemporary rational approximation methods. Once a reduced equation system has been specified, a method for their solution must be found. One can employ exact analytical meth- ods, asymptotic analytical methods, computational techniques, and even formal mathematical methods to find solutions as well as solution bounds, properties, and uniqueness. For most fluid-physics processes useful exact analytical solutions are seldom found. Asymptotic solu- tions provide a quantitative description of the physical phenomena for limited ranges of parameter values. In highly nonlinear problems (for example, chemically active systems) novel perturbation techniques are needed to find concise, uniformly valid expansion-based solutions. This is particulary important in systems with disparate time and length scales. Numerical simulation must include assessments of accuracy and resolution so that physically viable solutions are discriminated from those that represent numerical artifacts. Analytically derived asymp- totic solutions are not only useful as benchmarks to test numerical methods but also in providing the numerical time and length scales essential in resolving real physics. The need to benchmark numerical simulations is especially important when the numerical model employs the full equations describing the processes involved. In this case, the ensemble of physical processes occurring concurrently is large and the resolution of disparate length and time-scale processes is essential. Only in the area of turbulence is the mathematical modeling hindered by the lack of definitive conceptual models. Averaged equations derived from the Navier-Stokes equations always have undefined terms that are only described in terms of ad hoc closure approxima- tions. So far, mathematical methods have not yielded rationally derived rules for closure, and a more focused effort toward providing better answers to this question may prove fruitful. COMPUTATIONAL FLUID DYNAMICS In recent years rapid progress has been made in computational fluid dynamics. The moving force for this development was largely provided by the availability of reliable and powerful computer resources. This in turn has stimulated both theoretical and experimental research toward the understanding of fundamental processes in fluid dynamics. As a result, we currently have the capability to calculate many complex unsteady two-dimensional and steady three-dimensional flows in- cluding the effects of compressibility and viscosity that were impos
90 PLASMAS AND FL UlDS sible or impractical only a few years ago. There are, however, many limitations that must still be overcome. Computational aerodynamics has progressed during the last two decades from linear theory for slender-body-flow calculations to nonlinear inviscid theory for flows about aircraftlike configurations. During the last decade there has been much activity in calculating three-dimensional compressible viscous flows past relatively simple aerodynamic shapes using the Reynolds-averaged Navier-Stokes equa- tions with turbulence modeling. These calculations, representing the present stage of development, require only the space-time resolution of the gross turbulence effects and leave the representation of the remaining, although highly significant, turbulence effects to realistic modeling. The computer storage and speed requirements of this stage are much less than those of the next and final stage, which represents by mesh and time-step resolution all sizes of the significant energy- bearing turbulent eddies. With the present and very near future advances in computer technology and numerical method development, we are now on the threshold of extending the Reynolds-averaged calculations to full aircraft at flight conditions. To pass over this threshold into the practical use of such calculations for aircraft design requires the solution of several topological problems in fitting a system of mesh points about a geometric shape as complex as an aircraft configuration, the development of convergence acceleration proce- dures to enhance the efficiency of numerical methods for solving the equations of compressible viscous flow, and the implementation of solution-adaptive grid systems. Much progress is also required before the currently available turbu- lence models will be able to account for the effects of strongly interacting flow fields with moderate or large amounts of separation. There is no assurance that such capability will be forthcoming in the near or even distant future. However, present models can predict to engineering accuracy turbulence boundary-layer interactions with few or no regions of separation. Development of the procedures required to extend viscous flow calculations to complex three-dimensional flows, soon to be possible with forthcoming computers, without waiting for further improvements in turbulence modeling is still a logical next step. These calculations will also be of engineering accuracy for flows near design conditions and can be used to predict incipient separation, shock and vortex boundary-layer interactions, buffet, reduced lift, and interference phenomena. Improvements in turbulence modeling will further extend the range of application, eventually to tactical aircraft in maneuver.
FLUID PHYSICS 91 Within the next 2 years computer resources will become available that can process data at a rate of the order 5 x 108 floating-point operations per second two orders of magnitude faster than current machines with core memories exceeding 16 x 106 words. This capability will enable Reynolds-averaged Navier-Stokes calculations to be made about body shapes as complex as modern aircraft at the same cost and time as present calculations for fairly simple geometric shapes. Further improvements in reducing computer cost and time are required to make such calculations practical for aerodynamic design. However, complementary to advances in computer technology, new numerical methods are being developed to increase numerical effi- ciency. If this research continues at its present rate it is predicted that a fivefold increase in numerical efficiency will occur during the next 5 years and that a possible two-orders-of-magnitude speed increase is projected during the next 15 years for solving the equations of compressible viscous flow. EXPERIMENTAL METHODS Instrumentation Developments in fluid-dynamic instrumentation techniques over the past 10 years have involved combining extensive computer analysis with well-established techniques, such as conditional sampling of hot-wire probe outputs in the study of turbulence. There has also been an explosive application of laser techniques. For example, we have Raman scattering for rotational temperature, Doppler velocimeters, and excitation techniques (LIF, or laser-induced fluorescence) along with particle and droplet sizing instruments based on laser scattering. These techniques follow the historical trend in gas dynamics and combustion research of striving for ways to measure the energy budgets in fluid flows. The distribution of energy among the classical and quantum-mechanical states of a gas or fluid is fundamental to many areas of fluid-physics research. The newly developed techniques permit one to investigate flows in ways that have previously not been possible. The drawback of most of them is that they are relatively complicated and time-consuming to use. However, because of a convergence of developments in several fields (medical imaging, large-array processors) it is now possible to antici- pate a revolution in fluid-dynamic instrumentation. The ideal fluid-dynamic instrument is capable of approximately point resolution, is noninvasive, and can obtain data from a relatively large
92 PLASMAS AND FLUIDS volume of flow simultaneously and display it in arbitrary planes cut through the volume. Using the computer technology developed for axial tomography in medical imaging combined with single- and multiphoton excitation or scattering techniques in multiangular projec- tion geometry, it is possible to project that with significant support over the next few years many of the characteristics of the ideal fluid- dynamic instrument can be achieved. Note that advances in recent years, say in the identification and study of large-scale structures in turbulent flows, have relied heavily on flow visualization methods including painfully reconstructed information in plane cuts through flows using point-by-point measurements from a few probes. Subse- quently, the results are manipulated and displayed by a computer. Rapid collection of volume data is an essential part of improving wind-tunnel testing efficiencies since only then can full advantage be obtained from introducing on-line computational techniques into ex- perimental studies. There has been an explosion of instrumentation effort in the atmo- spheric sciences. Ground-based remote sensing now allows us to measure the turbulence structure of the atmosphere, showing internal waves, turbulence, clouds, severe storms, and jet streams in detail. The impact on theoretical studies has been great, with a new picture of mesoscale structure emerging. New developments in technology have also led to the development of new oceanographic sensors that drift with the sea motion and are interrogated by satellites. These are expected to provide a wealth of flow information in the next decade: One area where instrumentation is particularly important and dif- ficult is combustion research. In combustion we seem now to be in a period of active development of experimental techniques. Certain quantities that could not be measured 10 years ago currently can be measured routinely (e.g., rotational temperatures). There are a number of key quantities that cannot be measured today but are likely to be measurable routinely in 10 years (e.g., certain joint probability-density functions). A large fraction of the progress being made concerns optical techniques. Optical methods developed during the past 10 years include Raman spectroscopy (of various types) for measuring temperatures and con- centrations of various chemical species, Rayleigh scattering for mea- suring densities, laser-Doppler velocimetry for measuring velocities, resonance fluorescence for measuring radical concentrations, and laser holography for measuring temperature fields. Since combustion envi
FLUID PHYSICS 93 ronments are rather hostile, the remote nature of optical devices can possess importance beyond their obvious nonobtrusive benefits. Ca- pabilities in time and space resolution by optical methods have progressed to a point at which many quantities of interest in turbulent reacting flows can be measured on a space-time resolved basis. Much important knowledge has been obtained in recent years by application of optical techniques to studies of reacting flows in well-equipped laboratories. For example, the nature of the quench layers at the walls for applications in piston engines has been clarified to a large extent by these methods; and contrary to earlier belief, it was established that the wall-quench layer is not a source of unburned hydrocarbons. Progress of this type could not have been made without the new optical methods. There is still important information that is not fully accessible. For example, the joint probability-density functions for the concentration and the magnitude of the gradient of the concentration (effectively the so-called scalar dissipation rate) in turbulence diffusion flames plays a central role in theories of heat-release rates and of extinction, but no experimental information is yet available. This is just one example of measurement at the frontier of optical techniques in combustion. The results needed are quite likely to be obtained over the next 10 years. There are good prospects for continued improvement in capabilities of the optical methods. Moreover, there are theories in need of testing (and of input parameters) that can benefit from these improvements. Therefore, we can visualize experimental techniques (especially opti- cal techniques) in combustion to be an active area during the next 10 years. Flow Facilities Facilities associated with direct application of fluid mechanics, such as wind tunnels for airplanes, have always been available. The cryo- genic wind tunnels for obtaining high Reynolds numbers now being brought into use are a recent example of this historical trend in facility development for aerodynamic purposes. The current efforts to develop an adaptive wall or "smart" transonic wind tunnels is an indication that significant new aerodynamic facilities will come on-line in the next decade. It is difficult, however, to build significant facilities simply to investigate questions of fluid physics. It seems to us that there may be a need for facilities that are designed for and dedicated to the study of specific areas of the physics of fluid motion. We suggest that the
94 PLASMAS AND FL UlDS fluid-physics community be alert to possible needs in this area and, if appropriate, develop open discussion at the national meetings on this subject. It would be a benefit to fluid physics if unique national experimental facilities could be used on a regular basis by university and other researchers. We are of the opinion that such a program would inject new ideas into the organization operating the facility, as well as permit state-of-the-art experiments by a widened pool of talented researchers. Typically, large national facilities tends to be equipment rich compared with university laboratories. Providing access and attractive arrange- ments for conducting experiments by visiting investigators may be an efficient way to increase the productivity of these facilities. ACKNOWLEDGMENTS The panel members thank the following people for their contribu- tions of sections to this chapter: T. J. Hanratty, University of Illinois (Multiphase Flows); D. R. Kassoy, University of Colorado (Modeling and Analytical Methods); S. Leibovich, Cornell University (Stability); G. C. Pomraning, University of California, Los Angeles (Radiation Hydrodynamics) .