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When the sea surface is moderately wind roughened, typically by winds of 2.5 to 7.5 m/s (5 to 15 knots), synthetic aperture radar (SAR) images of ship wakes, obtained from aircraft or spacecraft, often appear as a long, narrow, dark streak against a brighter background. The dark streak images can have lengths of tens of kilometers at the lower end of the wind range. The spacecraft image of the ocean surface with the ship wake image shows that the visible length of the ship-wake image reaches about 100 km (Naval Air Warfare Center Aircraft Division, Waiminster, PA, 1992/ in Benilov (1994, 1997a)). 1.2. The Upper Layer Turbulence. The turbulent upper layer of the ocean has a complex vertical structure defined by influences of different physical mechanisms such as energy and momentum transfer, the presence of surface waves and their breaking, the turbulent energy production by mean shear flow, the wave motions of the fluid, and the effect of the Coriolis force. In contrast to atmospheric boundary layers over land, where mean velocity shear is the main source of turbulence energy, the turbulence in the upper layer of the ocean is governed not only by mean velocity shear, but also by surface waves. The transport of momentum, heat, moisture and salt occurs across the air-sea interface and is affected by the ocean surface waves. Therefore surface waves play an important role in the air-sea interaction system. The turbulent motion in the upper ocean is a highly specific example of turbulence in a liquid whose free surface is subject to wind friction. The result of this action is the formation of waves, pure drift currents and turbulence, which lead to strong vertical mixing of the surface layer. In contrast to boundary layers at a solid wall where mean velocity shear is the main source of the turbulent energy, the turbulence in the upper ocean is governed in many respects by the nature of waves. The total mean atmospheric stress not only induces ocean currents through the action of the shear stress alone but also supplies momentum to growing surface waves. A part of the momentum and energy is transferred directly from the wind to drift currents, while another part goes into surface waves. Wind waves contain a considerable amount of momentum and energy and they redistribute the momentum and energy over great distances and supply energy to drift currents and turbulence by their breaking. The wave breaking creates a highly turbulent environment within the top few meters of the ocean, and the wave dissipation by the breaking intensifies turbulence in the ocean mixed layer (Drenann et al., 1992). Wave breaking provides a mechanism for injection of both momentum and turbulent kinetic energy from the surface winds to the water. Experimental results indicate that the relative energy that is lost from the wave motion due to a single breaking lies between 10−2 and 10−1 (Melville and Rapp, 1985). The energy transferred per unit time from the wind to the water surface is an order of pure drift currents (Kitaygorodskiy, Miropolskiy, 1968; Kitaygorodskiy, 1970). Therefore, the turbulence of the upper ocean is nourished by the energy supplied from the waves. Consequently, the turbulence characteristics should depend on the state of the ocean surface. A moving ship leaves a long wake trail behind and makes it possible to monitor the traveling ships long range by means of radar systems. Turbulent sensors are also able to detect “in situ” the wake turbulence in the case of complex environment situation. Since the properties of a ship wake are expected to depend on the speed and size of the ship, theoretical study should be provided to analyze the wake properly. In the ocean, many natural atmospheric and oceanic features interact with the wake. Therefore, the natural ocean turbulence should be studied to identify the ship wake from an oceanic environment. 2. THEORETICAL MODEL 2.1. Wake Turbulence. A ship traveling with a constant speed is considered as an active source of turbulence, and the turbulence is developed within the boundary that is growing in time and characterizes the scale of the turbulence. To describe the dynamic behavior of the turbulence in the ship wake, the following assumptions are made (Benilov, 1994, 1997a): 1. The wake turbulent kinetic energy significantly exceeds the upper layer turbulence that reduces the turbulent wake problem to the turbulent region development in a non-turbulent liquid. 2. The main source of turbulence is a moving ship that means that all interactions between the wake turbulence and environment do not the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Us, Ua, m/s m/s Side View. 3 3, 5, 7, 10 Table 1. Conditions of the numerical experiments Figure 4. The Body of the Wake within Environmental Turbulence (Ua=5m/s). Equi-Kinetic Energy Isolines. 3D 7 3, 5, 7, 10 SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT Top View, b—Side View) 10 3, 5, 7, 10 normalized form conforms the theoretical and Milgrem's power law that well approximates experimental data. Figure 5. Ship-Wake Equi-Kinetic Energy Isolines (a— 695

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. cm/s. SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT Figure 8. Turbulent spectrums along the wake axis at different distances from the ship model. Figure 9. Turbulent spectrums in the wake cross section at the distance L=4.2 m from the model, model speed U s=68 697

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. cm/s. cm/s. SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT Figure 11. Turbulent spectrums in the wake cross section at the distance L=13 m from the model, model speed Us=202 Figure 10. Turbulent spectrums in the wake cross section at the distance L=8 m from the model, model speed Us=202 698

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. cm/s. s, wave elevation variance 2.54 cm, spectral peak frequency 1 Hz. SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT Figure 13. Wake turbulence under spectral waves conditions at distance L=13 m from the model, model speed 126 cm/ Figure 12. Turbulent spectrums in the wake cross section at the distance L=13 m from the model, model speed Us=68 699

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 700 5. CONCLUSION Theoretical base, numerical modeling and experimental study on ship wake detection in the ocean turbulent environment has been developed. All these studies demonstrate that the ship-wake turbulence is well detectable and Kolmogorov's range can be identified. The turbulent sensors can detect the wake turbulence in the case of complex environment situations and at significant distances from a ship. In case of strong wind conditions there is significant submerged wake body that can be detected by the turbulent sensors. We express our deep gratitude to the ADD of Republic of Korea for support of this work. REFERENCES Benilov, A.Yu., 1973, “The Turbulence Generation in the Ocean by Surface Waves”, Izv.Ac.Sci. USSR, Atm. Ocean Phys., V. 9; No. 3; pp. 160–164 (Translated in English). Benilov, A.Y., Lozovatsky, I.D., 1975. Spectral Models of the Oceanic Turbulence, In Monograph: Research of the Turbulent Structure of the Ocean, The Sea Hydrophysical Institute ed. AN USSR, Sevastopol, pp. 102–112. Benilov, A.Y., and Lozovatsky, I.D., 1977. Semi empirical Methods of the Turbulence Description in the Ocean, In Monograph: The Turbulence and Diffusion of the Ingredients in the Sea, The Co-Ordination Center of the COMECON (SEV), Information Bulletin, Vol. 5, Moscow, pp. 89–97. Benilov, A.Yu., T.G.McKee and A.S.Safray, 1993, “On the Vortex Instability of Linear Surface Wave”, In: Numerical Methods in Laminar & Turbulent Flow, Vol. VIII, part 2, Pineridge Press, U.K., pp. 1323–1334. Benilov, A.Y., 1994, A Discussion of the Turbulent Nature and Possible Causes of the Ship Wake Radar Image. TR-SIT-DL-9409–20704,. Stevens Institute of Technology, Hoboken, NJ, 49 pp. Benilov, A.Y., 1997(a), Ship—Wake Turbulence, In: NUMERICAL METHODS in LAMINAR & TURBULENT FLOW, vol. 10, Edited by: C.Taylor, University of Swansea, U.K., Pineridge Press. Benilov, A.Y., 1997(b), The Ocean Upper Layer With the Presence of the Surface Waves and Their Breaking, TR-SIT-DL-9707, Stevens Institute of Technology, Hoboken, NJ, 54 pp. Benilov, A.Y. and G.C.Bang, 1999, Ship Wake Detection in the Ocean Upper Layer, TR-SIT-DL-9904, Stevens Institute of Technology, Hoboken, NJ, 111 pp. Birkhoff G. and E.H.Zarantonello, 1957, “Jets, Wakes and Cavities”, Academic, San Diego, Calif. Drenann, W.M., K.K.Kahma, E.A.Terray, M.A. Donelan, and S.A.Kitaygorodskiy, 1992, “Observations of the enhancement of kinetic energy dissipation beneath breaking wind waves”, Edited by M.L.Banner and R.H.Grimshow, Springer—Verlag, New York, pp. 95–101. Hoekstra M., J. Th. Ligtelijn, 1991, “Macro wake features of range of ships”, Technical Report 410461–1-PV, Maritime research Institute Netherlands, Wageningen, The Netherlands. Hoffman Klaus A., 1989, “Computational Fluid Dynamics For Engineers”, A Publication of Engineering Education System, Austin, Texas. Kitaygorodskiy, S.A. and Yu. Z.Miropolskiy, 1968, “Dissipation of Turbulent Energy in the Surface Layer of the Ocean”, Izv. Acad. Sci. USSR, Atmospheric and Oceanic Physics, Vol. 4, No. 6, (Translated in English). Kitaygorodskiy, S.A., J.A.Lumley, 1983, “Wave-Turbulence Interactions in the Upper Ocean Part I: The Energy Balance of the Interacting Fields of Surface Wind Waves and Wind Induced Three Dimensional Turbulence”, J. of Physical Oceanography, Vol. 13, No. 11, pp. 1977–1987. Longuet-Higgins, M.S., 1969, “On the Wave Breaking and the Equilibrium Spectrum of wind-Generated Waves”, Proc. Roy. Soc., London, Vol. A310, No. 1501, pp. 151–159. Melville, W.K., and R.J.Rapp, 1985, Momentum flux in breaking waves, Nature, 317, 514–516, 1985. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 701 Melville, W.K., 1994, “Energy dissipation by breaking waves”, J. Phys. Oceanogr., 24, 2041–2049. Melville, W.K., 1996, “The role of surface-wave breaking in air—sea interaction”, Annual Review of Fluid Mechanics, Vol. 28, 279–321 Milgram J.H., R.D.Peltzer, and O.M.Griffin, 1993, “Suppression of Short Sea Waves in Ship Wakes: Measurements and Observations”, J. Geophysics Res. Vol. 98, No C4, pp7103–7114. Mohammadi B. and O.Pironneau, 1994, “Analysis of K-Epsilon Turbulent Model”, John Wiley & Sons, 196 pp. Monin A.S., A.M.Yaglom, 1965, “Statistical Hydromechanics: Turbulence Mechanics Part 1”, (1967, Part 2) Moscow, Fizmatgiz, pp. 639. (Fifth printing, 1987, Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1–2. The MIT Press) Naudascher, E., 1965, “Flow in the Wake of Self-Propelled Bodies and Related Sources of Turbulence”, J. Fluid Mech., V. 22, No. 1, pp. 625–656. Phillips O.M., 1966, “The Dynamics of the Upper Ocean”, Cambridge University Press. Poulter E.M., M.J.Smith, and J.A.McGregor, 1994, “Microwave backscatter from the sea surface: Bragg scattering by short gravity waves”, Journal of Geophysical Research, vol. 99, No. C4, pp. 7929–7943. Stewart, R., 1985, “Method of Satellite Oceanography”, Univ. of California Press, Berkley, 352pp. Tennekes, H. and J.L.Lumley, 1990, “A First Course in Turbulence”, 13th Printing, MIT Press, Cambridge, MA. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 702 DISCUSSION D.Savitsky Davidson Laboratory Stevens Institute of Technology, USA The authors present an excellent overview of the turbulent properties of ship wakes; ocean upper layer turbulence; and their interaction. Further, the results of their recent model tests of ship wake turbulence and wave turbulence measured separately and in combination (ship model running in head seas) are also presented. These experimental results (particularly the combination of ship wake and wave turbulence fields) appear to be unique and constitute a valuable contribution to the literature. I have two questions for the authors. Concerning the turbulent wake of the ship alone, it would be useful if the authors would identify the relative contributions of ship hull form; propulsor; and ship generated waves (which may break) to the total turbulent wake field. Visual examination of the surface wake aft of a ship gives the impression that the propulsor wake may dominate so that the particulars of the ship geometry may only be important in defining the propulsor thrust and the concentrated kinetic energy it imparts into a diameter of fluid which is substantially smaller than the beam of the ship. In any event it would be useful to understand the make-up of the term kw in their Equation (26) and how it relates to ship form, propeller performance (especially cavitation effects), breaking of ship generated waves, air entrainment and speed. Also, since that equation implies that the turbulent fields due to ship wake and waves are independent properties that are directly additive, does the model data indeed support this assumption? The second question concerns the turbulent properties of waves used in the authors' model tests. These waves are generated mechanically; have no atmospheric wind on their surface; are probably devoid of air entrainment, and likely are not continuously breaking. What is the authors' opinion on the characteristics of model wave turbulence fields vs. those in full-scale wind generated breaking waves? AUTHOR'S REPLY None received. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line SHIP WAKE DETECTABILITY IN THE OCEAN TURBULENT ENVIRONMENT 703 DISCUSSION K.Voliak Russian Academy of Sciences, Russia The reviewed paper consists of three sections: analytical, numerical, and experimental, united by a common idea to show the ship wake turbulence against a background turbulence of the upper ocean. The theoretical section is based on the assumption that the shear-free axisymmetrical unsteady turbulent motion with some scaling parameters spreads into a nonturbulent fluid. Then the Kolmogorov's self-similarity solutions are used to describe the cylindrical turbulent wake controlled by the ship beam, turbulence coefficient, and velocity, as well as by an experimentally determined eigenvalue of the corresponding boundary problem. The model of turbulence in the upper ocean is chosen as a quasisteady horizontally uniform random hydrodynamic field with account of surface waves (breaking, in general) and mean shear flow. The latter factors allow authors to separate three turbulent layers in the ocean medium vertical profile: wave-perturbed subsurface region, transitional diffusive interlayer, and underlying classical logarithmic mean-shear half-space. When using quite general estimates for the uppermost layer, the above vertical structure is presented in an explicit form. The result of performed analytical estimates, based on comparison of the wake and the medium turbulence, is presented in the form of technical formulas and diagrams containing ship and environment characteristics. Further in the section devoted to numerical simulation, the authors directly model the wake—upper ocean interaction by turbulent transport equations and present graphically a 3D structure of the ship wake depending on important controlling parameters of the source and environment. The experimental study with a propelled ship model in the laboratory tank, closing the paper, should, on authors' opinion, verify the developed theory and numerical calculations. In fact the wake turbulence spectra are rather thoroughly measured by a hot film anemometer across and along the tank behind the model. The anemometer sensitivity turns out sufficiently high to measure very weak turbulence signals, even against the background of specially generated surface waves. All the three approaches used by authors of the reviewed paper do not overlap some compact concept of the ship turbulent wake in the real ocean environment to an equal extend but rather complement each other. For example, no layered structure of turbulence, developed analytically, is shown evidently in numerical and laboratory experiments. However, the method of presentation used in the paper has own advantages to make perhaps the pattern of studied phenomenon more voluminous. Some questions can also arise, when reading the article. First, it would be desirable to take the sea wave directionality into account in the model of upper turbulence, in parallel to the wake axial scale, though this task is not too simple. Also the technical formulas derived can be readily simplified, for example, by lowering the accuracy in numerical factors and exponents, as well as by expanding or approximating some terms, etc. Second, on my opinion, it is important to widen the description of numerical model and the presentation of calculated data, in particular, to show both the simplifications based on the developed theory and a possible restructuring of the wake as it penetrates through the wave-perturbed zone into deeper layers. In the experimental section, it is not clear how were the surface waves excited in the tank, and in general the extensive wave modeling would be of crucial importance in view of the main problem posed in the work. An explanation of the experiment scaling seems also to be not superfluous. Besides, a general accent on numerics and experiments (maybe in oral presentation) can redistribute the reviewed material more symmetrically. As a whole, the discussed study is well-grounded and comprehensive, its results are reliable and interesting to researchers, especially such as data on the numerically modeled deepened ship wake. AUTHOR'S REPLY None received. the authoritative version for attribution.