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The surface layer for free-surface turbulent flows. (English) Zbl 0938.76044

Direct numerical simulation (DNS) is used to examine low Froude number free-surface turbulence (FST) over a two-dimensional mean shear flow. The Navier-Stokes equations are solved using a finite difference scheme with a grid resolution of \(128^3\). Twenty separate simulations are conducted to calculate the statistics of the flow. Based on the velocity deficit and the vertical extent of the shear of the mean flow, the Reynolds number is 1000 and the Froude number is 0.7. We identify conceptually and numerically the surface layer, which is a thin region adjacent to the free surface characterized by fast variations of the horizontal vorticity components. A promiment feature of FST is the vortex connection to the free surface which occur inside the surface layer. It is found that as hairpin-shaped vortex structures approach the free surface, their ‘head’ part is dissipated quickly in the surface layer, while two ‘legs’ connect them almost perpendicularly to the free surface. Analysis of the evolution of surface-normal vorticity based on vortex surface-inclination angle shows that both dissipation and stretching decrease dramatically after connection. Finally, we investigate the effect of non-zero Froude number on the turbulence statistics.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76M20 Finite difference methods applied to problems in fluid mechanics
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