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The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy. gan towing-tank facility even with the use of scrubbers3. 8CONCLUSIONSComparisons between the LES and DNS indicate that the LES should be performed at higher resolution to resolve a sufficient portion of the turbulent energy cascade. For the present low-resolution LES, the global stress model (Type II closure) provides excellent prediction of the SGS stresses, but the wavenumber content is too high to be resolved in a LES formulation. For the same resolution, a grid filter with no SGS model works as well as the closure models that we have tested to date. These trends require investigation at higher resolution. The next step in SGS modeling will also require a detailed study of the structure of turbulence [25, 27]. DNS studies of free-surface turbulence do not provide evidence that whirls will persist on the free surface due to the effects of two-dimensional turbulence at low Reynolds numbers. DNS studies show that free-surface roughness is proportional to the component of the pressure that is induced by the vortical portion of the flow. Since turbulent dissipation relative to turbulent scattering is a higher order function of the Froude number, its effects will diminish more rapidly in a ship wake. The turbulent scattering and dissipation of 5cm surface waves are dominated by the effects of parasitic capillary waves and surfactants for Froude numbers that would correspond to a region that is several ship lengths aft of the stern. These DNS results are tempered by our inability to resolve the free-surface boundary layer. We propose to overcome this problem by using the boundary-layer formulation of the free-surface boundary conditions that we provide in Equation (11). This boundary condition is already incorporated into our LES capability. The boundary-layer formulation enables us to simulate the dominate dissipative effects of parasitic capillary waves while still maintaining an ability to predict free-surface roughness, and turbulent scattering and dissipation. ACKNOWLEDGEMENTSThis research is financially supported by the Fluid Dynamics Program at the Office of Naval Research. E.A.N. is also supported by the Department of Energy. The numerical simulations have been performed on the CRAY Y-MP's at the Numerical Aerodynamic Simulation (NAS) Program and the Primary Oceanographic Prediction System (POPS), and the CM-5 at the Naval Research Laboratory. We are grateful to Dr. Thomas Lund at Nasa Ames Research Center, who provided us with the results of spectral computations. We are also indebted to Dr. Robert Hall at Science Applications International Corporation for his helpful discussions. References[1] Bardina, J., Ferziger, J.H., and Reynolds, W.C. ( 1980) Improved subgrid-scale models for large-eddy simulations. AIAA 80–1357. [2] Comte-Bellot, G. and Corrsin, S. ( 1971) Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated ‘isotropic' turbulence. J. Fluid Mech., 48, 273–337. [3] Cox, C.S. ( 1958) Measurements of slopes of high-frequency wind waves. J. Mar. Res, 16, 199–225. [4] Deardorff, J.W. ( 1970) A numerical study of three-dimensional turbulent channel-flow at large Reynolds numbers. J. Fluid Mech., 41, 453–480. [5] Dommermuth, D.G. ( 1992) The formation of U-shaped vortices on vortex tubes impinging on a wall with applications to free surfaces. Phys. Fluids, A bf 4(4), 757–769. [6] Dommermuth, D.G. ( 1993a) The laminar interactions of a pair of vortex tubes with a free surface . J. Fluid Mech., 246, 91–115. [7] Dommermuth, D.G. ( 1993b) The initialization of vortical free-surface flows. J. Fluids Eng. To appear.
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