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Journal Articles Physical Review Fluids Year : 2017

## Wave-induced vortex recoil and nonlinear refraction

(1, 2) , (1) , (1)
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Thomas Humbert
Sébastien Aumaître
• Function : Author
• PersonId : 989203
Basile Gallet
• Function : Author
• PersonId : 989210

#### 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.

#### Domains

Physics [physics]

### Dates and versions

cea-01599684 , version 1 (02-10-2017)

### Identifiers

• HAL Id : cea-01599684 , version 1
• DOI :

### Cite

Thomas Humbert, Sébastien Aumaître, Basile Gallet. Wave-induced vortex recoil and nonlinear refraction. Physical Review Fluids, 2017, 2, pp.094701. ⟨10.1103/PhysRevFluids.2.094701⟩. ⟨cea-01599684⟩

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