Deterministic wave forecasting with the Zakharov equation

Abstract

This study investigates deterministic wave forecasting from the perspective of the Zakharov equation. Forecasts based on linear dispersion, weakly nonlinear amplitude dispersion, and the Zakharov equation are compared for reference ocean surfaces generated from JONSWAP and Pierson-Moskowitz spectra. This approach allows for the role of nonlinearity to be isolated, and demonstrates the success of simple frequency corrections in forecasting wave-fields up to moderate steepness. The role of second-order bound waves is investigated by means of analytical formulae, and their impact on forecast accuracy is illustrated for a range of forecast times.