Interaction of a deformable free surface with statistically steady homogeneous turbulence

Abstract

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.