Turbulence-induced anti-Stokes flow: experiments and theory

TL;DR

This study demonstrates experimentally and theoretically how surface waves interacting with sub-surface turbulence generate an Eulerian-mean flow that opposes Stokes drift, affecting water transport in oceans.

Contribution

It provides the first combined experimental and theoretical analysis of turbulence-induced anti-Stokes flow, revealing a new equilibrium state and a model based on Rapid Distortion Theory.

Findings

Eulerian-mean flow opposes Stokes drift near the surface

Flow reaches a new equilibrium with a specific ratio of velocity gradients

Stronger turbulence accelerates the growth of the Eulerian-mean current

Abstract

We report experimental evidence of an Eulerian-mean flow, $\overline{u}(z)$, created by the interaction of surface waves and tailored ambient sub-surface turbulence, which partly cancels the Stokes drift, $u_s(z)$, and present supporting theory. Water-side turbulent velocity fields and Eulerian-mean flows were measured with particle image velocimetry before vs after the passage of a wave group, and with vs without the presence of regular waves. We compare different wavelengths, steepnesses and turbulent intensities. In all cases, a significant change in the Eulerian-mean current is observed, strongly focused near the surface, where it opposes the Stokes drift. The observations support the picture that when waves encounter ambient sub-surface turbulence, the flow undergoes a transition during which Eulerian-mean momentum is redistributed vertically (without changing the depth-integrated mass transport) until a new equilibrium state is reached, wherein the near-surface ratio between $|\mathrm{d}\overline{u}/\mathrm{d}z|$ and $|\mathrm{d}u_s/\mathrm{d} z|$ approximately equals the ratio between the streamwise and vertical Reynolds normal stresses. This accords with a simple statistical theory derived here and holds regardless of the absolute turbulence level, whereas stronger turbulence means faster growth of the Eulerian-mean current. We present a model based on Rapid Distortion Theory which describes the generation of the Eulerian-mean flow as a consequence of the action of the Stokes drift on the background turbulence. Predictions are in qualitative, and reasonable quantitative, agreement with experiments on wave groups, where equilibrium has not yet been reached. Our results could have substantial consequences for predicting the transport of water-borne material in the oceans.