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Article Dans Une Revue Journal of Fluid Mechanics Année : 2017

Two-dimensional stability of finite amplitude gravity waves on water of finite depth with constant vorticity

Résumé

A numerical investigation of normal-mode perturbations of a two-dimensional periodic finite-amplitude gravity wave propagating on a vertically sheared current of constant vorticity is considered. For this purpose, an extension of the method developed by Rienecker & Fenton (1981) is used for the numerical computations of the finite amplitude waves on a linear shear current. This method enables to compute accurately waves with or without critical layers and pressure anomalies. The numerical results of the linear stability analysis extend the weakly nonlinear, analytical results of Thomas et al. (2012) to fully nonlinear waves. In particular, the restabilization of the Benjamin-Feir modulational instability, whatever the depth, for an opposite shear current is confirmed. For these side-band instabilities, the numerical results show some deviations with the weakly nonlinear theory as the wave steepness of the basic wave and vorticity are increased. Besides the modulational instabilities new instability bands corresponding to quartet and quintet instabilities, which are not side-band disturbances, are discovered. The present numerical results show that with opposite shear currents increasing the shear reduces the growth rate of the most unstable side-band instabilities, but enhances the growth rate of these quartet instabilities, which eventually dominate the Benjamin-Feir modulational instabilities.
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Dates et versions

hal-01793103 , version 1 (16-05-2018)

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Marc Francius, Christian Kharif. Two-dimensional stability of finite amplitude gravity waves on water of finite depth with constant vorticity . Journal of Fluid Mechanics, 2017, ⟨10.1017/jfm.2017.603⟩. ⟨hal-01793103⟩
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