Anomalous wave statistics induced by abrupt depth change

Abstract

Laboratory experiments reveal that variations in bottom topography can qualitatively alter the distribution of randomized surface waves. A normally-distributed, unidirectional wave field becomes highly skewed and non-Gaussian upon encountering an abrupt depth transition. A short distance downstream of the transition, wave statistics conform closely to a gamma distribution, affording simple estimates for skewness, kurtosis, and other statistical properties. Importantly, the exponential decay of the gamma distribution is much slower than Gaussian, signifying that extreme events occur more frequently. Under the conditions considered here, the probability of a rogue wave can increase by a factor of 50 or more. We also report on the surface-slope statistics and the spectral content of the waves produced in the experiments.