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Oceanography in 2025: Proceedings of a Workshop
Simulations of Marine Turbulence and Surface Waves: Potential Impacts of Petascale Technology
Peter P. Sullivan*
PETASCALE COMPUTING
Large scale parallel computing is a potential boon to the scientific interests of the geoscience communities and in particular oceanography. Over the next decade, computing systems will routinely attain peak speeds of one petaflop and more (1015 floating point operations per second) with memory capacities of order one petabyte (1015 bytes of information). This is at least an order of magnitude increase compared to the current generation of parallel machines (e.g., the IBM SP6 and Blue/Gene machines, see http://www.top500.org/ for current trends in supercomputing as well as the current ranking of the most powerful machines). An example of a peta-class system under development is the “Blue Waters” Project (http://www.ncsa.uiuc.edu/BlueWaters) being pursued by the National Center for Supercomputing Applications. Blue Waters aims to achieve sustained petaflop performance utilizing 106 computational cores and is projected to come online by 2011. By embracing petascale computational technology (recent developments in both hardware and software are described at http://www.image.ucar.edu/Workshops/TOY2008/focus2) early in its development phase oceanography will be in an advantageous position to advance its science and applications as even more powerful computational systems are developed.
*
University Corporation of Atmospheric Research
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Oceanography in 2025: Proceedings of a Workshop
SCIENCE AND APPLICATIONS
Current computational systems and algorithms allow DNS and LES of turbulent boundary layers utilizing O(10243 ~ 20483) gridpoints (see Figure 1). The majority of these calculations are posed in idealized settings with imposed external forcings (i.e., with no feedback or coupling to the larger scales). These calculations are interesting and enlightening, but do not adequately capture the full set of scale interactions. Future petascale computations are likely to use as many as O(10,0003) gridpoints and thus couple a wider spectrum of scales. These meshes will allow DNS and LES of marine boundary layers with higher Reynolds number incorporating numerous physical processes in larger domains. Strongly stable boundary layers (see Figure 2) are an important flow regime not currently addressed by either DNS or LES. Weak highly intermittent turbulence cannot be sustained in low Reynolds number DNS and in the current generation of LES with subgrid-scale (SGS) models that are too dissipative to capture the stochastic dynamics of high Reynolds number strongly stratified turbulence. At least an order of magnitude increase in Reynolds number along with further developments in SGS models are required to increase the fidelity of DNS and LES of stable boundary layers. Increases in computer power will also allow turbulent simulations over 3D topography, moving surface wave fields, and ocean boundary layers driven by hur-
FIGURE 1 Computational time per gridpoint for LES of a convective atmospheric boundary layer on a Cray XT4. a) left line and symbols problem size 5123; b) center line and symbols 10243; c) right lines and symbols 20483; and d) right diamond symbol 30723. The parallelization is accomplished using 2D domain decomposition and the Message Passing Interface (MPI), results from Sullivan and Patton (2008).
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Oceanography in 2025: Proceedings of a Workshop
FIGURE 2 LES of a nocturnal stable (atmospheric) boundary layer with mesh resolution ~ 2 m in all directions. The boundary layer depth zi ~ 200 m and the stability measure zi/L ~ 1.2 indicates a weakly stable regime (L is the Monin-Obukhov length). The 3D visualization of the vertical velocity field shows that the flow is dominated by numerous small scale structures. The vertical profile of the mean wind shows the formation of a super geostrophic jet near the top of the boundary layer and the stair-step structure in the vertical heat flux profile is suggestive of Kelvin-Helmholtz overturning. Strongly stable boundary layers, zi/L > 2, with intermittent turbulence are not adequately simulated with current LES and DNS.
ricane winds (see Figure 3). All these simulations will ultimately improve climate and weather forecasts.
Air-sea interaction and in particular the coupling of winds, waves, and currents at scales ranging from centimeters to kilometers is a fundamental scientific problem that is also likely to benefit from petascale computing. In order to more faithfully capture the dynamics of air-sea interaction the community should devote energy towards developing large-wave simulation (LWS) technology. LWS is viewed as a more complete cousin to today’s LES. A 3D time-dependent LWS model of the air-water interface would naturally capture interactions between winds, waves, and currents. An LWS model is cast in physical space by applying a spatial filter to the governing Navier-Stokes equations for an air-water medium including the proper kinematic and dynamic boundary condi-
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Oceanography in 2025: Proceedings of a Workshop
FIGURE 3 Variation of the vertical profile of turbulent scalar flux ‹w′θ› (z,t) from LES of an ocean boundary layer driven by Hurricane Frances winds and stresses. LES domains are located on the resonance (panel a) and non-resonance (panel b) sides of the storm track. At each time, the scalar flux is normalized by its imposed surface value. In these figures the ocean boundary layer (OBL) depth h, determined as the location of the maximum vertical temperature gradient, is shown as a heavy black line. The arrow shows the normalized entrainment flux (~−0.2) for a classical daytime convective atmospheric boundary layer (ABL). The contours of scalar flux show that the bulk of the temperature decrease in the ocean boundary layer is induced by entrainment cooling. The rapid oscillations in the scalar flux below the thermocline result from a complex system of internal waves excited by the strong wind forcing. The LES mesh is 500 × 500 × 160 gridpoints and the timestep ∆t varies from 15 s to 0.5 s over the length of the simulation. The total number of timesteps > 150,000.
tions at the air-water interface similar to LES. The filtering step introduces new unknown SGS terms, both turbulence-turbulence and turbulence-wave correlations, that need to be parameterized in terms of resolved winds, waves, and currents. Modeling these correlations is a challenging task and requires guidance from both laboratory and field measurements-
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Oceanography in 2025: Proceedings of a Workshop
spatial measurements of turbulence and waves in two different media are needed to validate and construct the needed SGS parameterizations. High resolution idealized DNS will be used to gain insight into the variations of these SGS correlations at lower Reynolds numbers. Efficient (and parallel) Poisson solvers are required to make LWS viable.
LWS will replace the current generation of spectral wave models which are largely built with heavy doses of empiricism for the wind input and dissipation source functions. LWS will answer fundamental questions as to how waves grow and the dependence on wave age and wave slope for a spectrum of waves. LWS might also prove useful in hurricane simulations. Also, LWS will permit testing of the fundamental interactions between waves and currents (e.g., Craik-Leibovich asymptotics can be tested). It will also provide insight into wave breaking dynamics, in particular the intermittent spatial and temporal distribution of breaking, and the generation of currents. A key aspect of LWS is the ability to integrate the equations of motion over sufficiently long periods so that waves grow, break and interact (i.e., the integration period is sufficiently long to permit significant wave-wave interactions). LWS will be complementary to simpler free surface calculations and will shed light on the important aspects of gas transfer related to micro-scale breaking.
REFERENCE
Sullivan and Patton. 2008. 18th Conference on Boundary Layer and Turbulence.
