Anomalous wave statistics induced by abrupt depth change

TL;DR

This study demonstrates how abrupt bottom depth changes in water can significantly alter wave statistics, increasing the likelihood of extreme rogue waves and changing the distribution from Gaussian to gamma.

Contribution

The paper provides experimental evidence that abrupt depth transitions induce non-Gaussian wave distributions and significantly elevate rogue wave probabilities.

Findings

Wave distribution shifts from Gaussian to gamma after depth change

Extreme wave events become 50 times more probable

Wave statistics downstream follow a gamma distribution

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.