Wave-induced vortex recoil and nonlinear refraction

TL;DR

This study investigates how surface waves induce vortex distortion, causing vortex center shifts and vorticity reduction, with experimental results supporting a model based on Stokes drift effects and vortex line dynamics.

Contribution

It introduces a simple vortex line model explaining wave-induced vortex shifts and vorticity expulsion, supported by experimental data and theoretical analysis.

Findings

Vortex center shifts transversely due to wave interaction.

Surface vorticity decreases inversely with Stokes drift.

Refraction angle diminishes with increasing wave intensity.

Abstract

When a vortex refracts surface waves, the momentum flux carried by the waves changes direction and the waves induce a reaction force on the vortex. We study experimentally the resulting vortex distortion. Incoming surface gravity waves impinge on a steady vortex of velocity $U_0$ driven magneto-hydrodynamically at the bottom of a fluid layer. The waves induce a shift of the vortex center in the direction transverse to wave propagation, together with a decrease in surface vorticity. We interpret these two phenomena in the framework introduced by Craik and Leibovich (1976): we identify the dimensionless Stokes drift $S=U_s/U_0$ as the relevant control parameter, $U_s$ being the Stokes drift velocity of the waves. We propose a simple vortex line model which indicates that the shift of the vortex center originates from a balance between vorticity advection by the Stokes drift and self-advection of the vortex. The decrease in surface vorticity is interpreted as a consequence of vorticity expulsion by the fast Stokes drift, which confines it at depth. This purely hydrodynamic process is analogous to the magnetohydrodynamic expulsion of magnetic field by a rapidly moving conductor through the electromagnetic skin effect. We study vorticity expulsion in the limit of fast Stokes drift and deduce that the surface vorticity decreases as $1/S$, a prediction which is compatible with the experimental data. Such wave-induced vortex distortions have important consequences for the nonlinear regime of wave refraction: the refraction angle rapidly decreases with wave intensity.