Deformations to a free surface by sub-surface zero-mean-flow turbulence

Turbulence in the bulk of an open-surface flow produces fluctuations in the elevation of the liquid surface above. As turbulent motions from the bulk reach the surface, they produce deformations according to a balance between their kinetic energy and the restoring effects of gravity and surface tension. Once produced, the deformations’ dynamics on the surface are complicated by their dispersion as capillary-gravity waves.

We characterize turbulence-induced free-surface deformations experimentally in a zero-mean-flow water tank in which turbulence is produced by arrays of randomly-actuated synthetic jets, spanning turbulence Reynolds numbers between 1000 and 8000, Froude numbers between 0.01 and 0.09, and Weber numbers between 0.2 and 8, with all parameters based on integral-scale quantities in the bulk. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence are used to relate the local surface deformation to the sub-surface vertical turbulent velocity and its vertical gradient in a vertical plane reaching multiple integral scales beneath the surface, enabling correlations between the deformation and velocity statistics over the entirety of the so-called source layer, in which the turbulence feels the surface’s presence. Secondly, PIV is performed in surface-parallel planes at various depths concurrently with a background-oriented schlieren measurement, which provides a map of the surface deformations above the recorded motions.