Experimental investigation relating free-surface features to sub-surface turbulence

Turbulent flows beneath a free surface play a central role in the Earth system, yet their coupling to observable surface features remains incompletely understood. Recent studies using Direct Numerical Simulations (DNS) have reported strong correlation between observable surface features and surface divergence as well as velocity statistics directly beneath, but were limited to Reynolds numbers ($Re$) far below those typical of natural flows, and do not carry the inherent challenges of measurement and flow fidelity that real flows present. We present a laboratory study in which free-surface topology and sub-surface turbulent velocity are measured simultaneously in a jet-stirred tank, extending these numerical results to the physical domain. Using a novel combination of particle-image velocimetry (PIV) and free-surface profilometry, we access $Re$ up to two orders of magnitude higher than in the DNS. A computer vision method developed for identifying turbulent imprints on the free surface is successfully applied to experimental data, enabling direct comparison with the DNS. The correlation between time series of mean-square surface divergence and surface features is found to persist as strongly at higher Reynolds numbers, despite the increased disparity of turbulent scales. Beyond the thin viscous layer, all surface-to-bulk correlations scale with the integral length scale across both experimental and numerical cases. The normalized cross-correlation between mean-square horizontal velocity divergence and surface area covered by structures decreases linearly with depth and remains significant even two integral scales beneath the surface, unlike point-to-point correlations which decay fast, illustrating how correlations are near-instantaneous but spatially non-local. These results demonstrate that visible surface features provide considerable... [truncated due to arXiv length constraint]