Effects of nonlinear energy transfer on short surface waves

The effects of nonlinear energy transfer on the development of the short wave spectrum are evaluated using a diffusion approximation and a modification of this approximation to include nonlocal effects. Both formulations were used to compute the evolution of a JONSWAP‐type spectrum, and the results are compared with direct numerical simulations. Terms corresponding to each of these formulations were then incorporated into the wave action equation, and the resulting equation was numerically integrated using a second‐order Runge‐Kutta method. The results show an increase in the angular width of the spectrum and in the spectral density at high wave numbers as compared with solutions of the action equation without the nonlinear energy transfer term. Example results are presented for the case of a moderately strong internal wave in a light wind, and implications for the remote sensing of these waves using microwave radar are discussed.