On the dissipation rate of ocean waves due to white capping

We calculate the rate of ocean wave energy dissipation due to white capping 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 only for moderate values of the surface steepness, $\mu < 0.09$. 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 the steepness. The results of both experiments are close. The white capping is the threshold process that takes place if the average steepness $\mu > \mu_{\mathrm{cr}}\simeq 0.055$. The rate of energy dissipation grows dramatically with increasing 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 the steepness.