Structure and energy transfer in homogeneous turbulence below a free surface

TL;DR

This study explores turbulence beneath a free surface, revealing how surface effects influence energy transfer and scale interactions, with findings that challenge existing theories and highlight the role of surface-induced structures.

Contribution

It demonstrates the impact of surface proximity on turbulence energy transfer, showing inverse cascades and scale growth not predicted by classical theories, using advanced PIV measurements.

Findings

Vertical and horizontal energy contributions align with rapid distortion theory at high Reynolds numbers

Horizontal integral scale increases near the free surface, contrary to classical predictions

Surface structures like upwellings and downwellings significantly influence energy transfer processes

Abstract

We investigate the turbulence below a quasi-flat free surface, focusing on the energy transport in space and across scales. We leverage a large zero-mean-flow tank where homogeneous turbulence is generated by randomly actuated jets. A wide range of Reynolds number is spanned, reaching sufficient scale separation for the emergence of an inertial sub-range. Unlike previous studies, the forcing extends through the source layer, though the surface deformation remains millimetric. Particle image velocimetry along a surface-normal plane resolves from the dissipative to the integral scales. The contributions to turbulent kinetic energy from both vertical and horizontal components of velocity approach the prediction based on rapid distortion theory as the Reynolds number is increased, indicating that discrepancies among previous studies are likely due to differences in the forcing. At odds with the theory, however, the integral scale of the horizontal fluctuations grows as the surface is approached. This is rooted in the profound influence exerted by the surface on the inter-scale energy transfer: along horizontal separations, the direct cascade of energy in horizontal fluctuations is hindered, while an inverse cascade of that in vertical fluctuations is established. This is connected to the structure of upwellings and downwellings. The former, characterized by somewhat larger spatial extent and stronger intensity, are associated to extensional surface-parallel motions. They thus transfer energy to the larger horizontal scales, prevailing over downwellings which favour the compression (and concurrent vertical stretching) of the eddies. Both types of structures extend to depths between the integral and Taylor microscales.