Title: Wave-induced vortex recoil and nonlinear refraction,
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.