A numerical study of the modulation of ShortSea waves by longer waves

The spatial spectrum of short sea waves is locally modulated by the presence of longer waves or currents; in the remote sensing literature, this process is described by the hydrodynamic modulation transfer function (HMTF). Such modulations are important in understanding radar images of sea waves with water wavelengths longer than the radar range resolution. Existing models for the HMTF utilized in remote sensing are based on approximations derived from consideration of conservation of wave action. However, the accuracy of these approximations has been quantified only through comparison with experimental data; in such comparisons, numerous empirical models for terms such as wind forcing and breaking wave dissipation are required, which make direct evaluation of the hydrodynamic effects difficult. A method for providing direct insight into the hydrodynamic modulation of short sea waves by longer waves is described in this paper, through use of numerical nonlinear hydrodynamic codes for sea surface evolution. The codes applied are reviewed, and a Monte Carlo simulation process based on a stochastic spectrum of short waves propagating over a single deterministic long wave is described, including the data analysis techniques developed to extract a numerical HMTF from the simulated surfaces. HMTF values obtained from the simulations are compared with those from a first-order wave action solution and are found to be in reasonable agreement, although differences on the order of 10% are observed. A numerical evaluation of long wave effects on the short wave dispersion relation is also provided.