New absorbing layers conditions for short water waves

Abstract : We develop a new PML formulation for the linearized shallow-water equations including the Coriolis force. The construction process is based on the uncoupling of the velocity components with the depth of water. Then the damping effect is only applied to the propagative modes just as was formerly done by Nataf \cite {Nataf} to the linearized Euler equations to enforce the long-time stability. We assess numerically the performance of the new absorbing condition and we illustrate in particular that it is stable for long-time simulations.