Note on a Modification to the Nonlinear Schrodinger Equation for Application to Deep Water Waves

K. B. Dysthe

Abstract

The ordinary nonlinear Schrodinger equation for deep water waves, found by perturbation analysis to O($\epsilon^3$) in the wave-steepness $\epsilon$ = ka, is shown to compare rather unfavourably with the exact calculations of Longuet-Higgins (1978b) for $\epsilon$ > 0.15, say. We show that a significant improvement can be achieved by taking the perturbation analysis one step further O($\epsilon^4$). The dominant new effect introduced to order $\epsilon^4$ is the mean flow response to non-uniformities in the radiation stress caused by modulation of a finite amplitude wave.