Turbulence beneath a free surface: boundary-induced modification and capillary-gravity wave turbulence

We present results from experiments capturing the interaction between homogeneous turbulence and the free surface above it, focusing on (a) the modification to the statistical properties of the bulk turbulence and the spatial and inter-component fluxes of energy and (b) the gravity-capillary waves devolving from the turbulence’s imprint on the surface.

Hydrodynamic turbulence is measured with particle image velocimetry (PIV) taken in surface-normal and surface-parallel planes, evidencing a re-partitioning of energy between velocity components by the surface, largely explained by rapid distortion theory. Surface deformations are simultaneously measured by background oriented schlieren imaging. We find a clear coupling between the concurrent surface deformations and sub-surface velocity structures: dimples in the surface are locked above intense surface-attached vortices. Less organized deformations from upwellings (fluid from the bulk impinging on the surface) propagate away as gravity-capillary waves. The spectrum of surface deformation extends to much smaller and shorter-duration scales than those forced by the turbulence, which is explained by non-linear interactions between surface waves building up a state of wave turbulence.