The current-modified nonlinear Schrodinger equation

By comparison with both experimental and numerical data, Dysthe's (1979) O( epsilon(4)) modified nonlinear Schrodinger equation has been shown to model the evolution of a slowly varying wavetrain well (here epsilon is the wave steepness). In this work, we extend the equation to include a prescribed, large-scale, O(epsilon(2)) surface current which varies about a mean value. As an introduction, a heuristic derivation of the O(epsilon(3)) current-mo dified equation, used by Bakhanov et al. (1996), is given, before a more fo rmal approach is used to derive the O(epsilon(4)) equation. Numerical solut ions of the new equations are compared in one horizontal dimension with tho se from a fully nonlinear solver for velocity potential in the specific cas e of a sinusoidal surface current, such as may be due to an underlying inte rnal wave. The comparisons are encouraging, especially for the O(epsilon(4) ) equation.