SHEAR-FREE TURBULENCE NEAR A FLAT FREE-SURFACE

In this study the evolution of initially homogeneous and isotropic tur bulence in the presence of a free surface was investigated. The Navier -Stokes equations were solved via direct pseudo-spectral simulation wi th a resolution of 96(3). The Reynolds number based on the volume-aver aged turbulence kinetic energy and dissipation rate was 147. Periodic boundary conditions were used in two dimensions, and the top and botto m sides of the domain were flat and shear-free. A random, divergence-f ree velocity held with a prescribed spectrum was used as the initial c ondition. An ensemble of sixteen separate simulations was used to calc ulate statistics. Near the surface, the Reynolds stresses are anisotro pic and the anisotropy extends a distance from the surface roughly equ al to the turbulent lengthscale. The tangential vorticity fluctuations also vanish near the surface, owing to the no-shear condition, causin g a corresponding decrease in the fluctuating enstrophy. The thickness of the region in which the surface affects the vorticity distribution is roughly one-tenth the turbulent lengthscale. The stress anisotropy near the surface appears to be maintained by reduced dissipation for the tangential velocity fluctuations, reduced pressure-strain transfer from the tangential to surface-normal velocity fluctuations, and rapi d decay of the surface-normal velocity fluctuations due to dissipation . The turbulence kinetic energy rises in the near-surface region owing to a decrease in dissipation at the surface. This decrease in dissipa tion results from the local reduction in enstrophy owing to the vanish ing of the tangential vorticity fluctuations at the surface. At the fr ee surface, the mean pressure rises. This is also due to the reduction in enstrophy. While the tangential vorticity must vanish at the free surface, the how is fully three-dimensional up to the surface and the production of surface-normal vorticity by vortex stretching attains a maximum at the free surface. The contribution to the total enstrophy b y the surface-normal vorticity fluctuations remains relatively constan t over depth. The production of the surface-normal enstrophy component due to vortex stretching is roughly balanced by turbulent transport o f enstrophy away from the surface. Near the surface, there an elevated levels of production of tangential vorticity by both vortex-stretchin g and fluctuating shear strains.