Subgrid scale structure of turbulence subject to surface wave straining*

The subgrid-scale (SGS) stresses and energy fluxes of a turbulent flow underneath a surface wave are investigated with direct numerical simulation. The SGS stresses is decomposed into three parts: the wave induced stress, the cross-interaction stress and the turbulent SGS stress. The turbulent SGS stress and other purely turbulence-related statistics are found to be weakly dependent on the wave shape range. Decomposition of the energy flux shows that an eddy-viscosity model is suitable for the turbulent SGS stress but is incapable of modeling the wave induced stress due to its different wavenumber with the wave induced straining. The budget equations for the filtered kinetic energy and the SGS kinetic energy are subdivided through the velocity partition, showing that direct energy transfer between scales only occurs within the same type of motion (wave induced motion or turbulence). The transport terms play an important role in the budget equation for the turbulent SGS kinetic energy.