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 properties of surface gravity waves in water of finite depth is discussed by analyzing laboratory experiments, field measurements, and numerical simulations to assess the role of modulational instability on wave statistics and particularly on the occurrence of extremes. Despite evidence of modulational instability in regular wave fields, results presented herein seems to indicates that wave instability has a negligible effect on wave statistics, which remains primarily affected by second-order contributions.