On Dissipation Rate of Ocean Waves due to White Capping

TL;DR

This study uses numerical simulations to analyze ocean wave energy dissipation due to white capping, revealing a steepness threshold and that existing models overestimate dissipation rates.

Contribution

It provides a detailed numerical comparison of two models for wave dissipation, identifying a critical steepness threshold and quantifying overestimations in current operational models.

Findings

White capping occurs when wave steepness exceeds ~0.055.

Energy dissipation rate increases sharply with steepness.

Operational models overestimate dissipation by about an order of magnitude.

Abstract

We calculate the rate of ocean waves energy dissipation due to whitecapping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve the $3D$ Hamiltonian equation that includes three- and four-wave interactions. This model is valid for moderate values of surface steepness only, $\mu < 0.09$. Then we solve the exact Euler equation for non-stationary potential flow of an ideal fluid with a free surface in $2D$ geometry. We use the conformal mapping of domain filled with fluid onto the lower half-plane. This model is applicable for arbitrary high levels of steepness. The results of both experiments are close. The whitecapping is the threshold process that takes place if the average steepness $\mu > \mu_{cr} \simeq 0.055$. The rate of energy dissipation grows dramatically with increasing of steepness. Comparison of our results with dissipation functions used in the operational models of wave forecasting shows that these models overestimate the rate of wave dissipation by order of magnitude for typical values of steepness.