Effect of shoaling length on rogue wave occurrence

TL;DR

This study investigates how the length of a coastal shoal influences rogue wave formation, revealing that slope steepness primarily drives rogue wave amplification rather than shoaling length, through theoretical and nonlinear simulation analyses.

Contribution

The paper develops a theoretical model and nonlinear simulations to distinguish the effects of shoal slope length and gradient on rogue wave occurrence, highlighting the dominance of slope magnitude.

Findings

Non-equilibrium dynamics dominate for steep slopes and large shoaling lengths.

Shoal slope steepness has a greater impact on rogue wave amplification than shoaling length.

Wave spectrum cutoff frequency and boundary conditions significantly influence wave statistics.

Abstract

The impact of shoaling on linear water waves is well-known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the "rapid'" nature of the shoaling process, i.e., shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through the development of a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the slope length and the slope gradient of a shoal and focus on the slope length to investigate the rapidness of the shoaling process on the evolution of key statistical and spectral sea-state parameters. Provided the shoal slope is 1/10 or steeper, our results indicate that the non-equilibrium dynamics is involved even for rather short shoaling lengths and becomes dominant in the regime of large lengths. When the non-equilibrium dynamics governs the wave evolution, further extending the slope length no longer influences the statistical and spectral measures. Thus, the shoaling effect on rogue waves is mainly driven by the slope magnitude rather than the slope length. Moreover, the simulations show that a higher cut-off frequency of the wave spectrum has a smaller impact on wave statistics than expected for a flat bottom in deep water and that insufficient attenuation of low-frequency waves at the downstream domain boundary has notable influence on wave statistics atop the shoal.