Rogue events in spatio-temporal numerical simulations of unidirectional waves in basins of different depth

TL;DR

This study numerically investigates rogue wave formation in unidirectional sea surface waves across various depths, revealing asymmetries, lifetimes up to 60 wave periods, and agreement with Baltic Sea observations.

Contribution

It provides new insights into rogue wave characteristics and their dependence on water depth using numerical simulations of the Euler equations.

Findings

Asymmetry between front and rear rogue wave slopes identified.

Rogue wave lifetimes can reach 30-60 wave periods.

Maximum wave height observed is about 3 times the significant wave height.

Abstract

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatio-temporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases ($k_p h > 0.8$, where $k_p$ is the peak wavenumber, and $h$ is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths. The lifetimes of rogue events may reach up to 30-60 wave periods depending on the water depth. The maximum observed wave has height of about 3 significant wave heights. A few randomly chosen in-situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.