Modulational instability and rogue waves in finite water depth

Abstract

Abstract. The mechanism of side band perturbations to a uniform wave train is known to produce modulational instability and in deep water conditions it is accepted as a plausible cause for rogue wave formation. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates this instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative water depths kh ≤ 1.36 (where k represents the wavenumber of the plane wave and h the water depth), but it can still destabilise due to oblique perturbations. Using direc..