Occurrence of extreme waves in finite water depth

Abstract

For random unidirectional wave fields propagating on water of infinite depths, high-order nonlinearity such as modulational instability is responsible for strong departures from Gaussian-and second-order-based statistics. For finite water depth, on the contrary, wave instability attenuates and eventually vanishes for relative water depths as low as kh = 1.36 (where k is the wavenumber of the dominant waves and h the water depth). Experimental results, nonetheless, indicates that oblique (directional) perturbations are capable of triggering and sustaining modulational instability and possibly lead to a wave amplitude growth even if kh < 1.36. Here a comparative analysis of the statistical pro..