NUMERICAL COMPUTATION OF STEEP GRAVITY-WAVES IN SHALLOW-WATER

An efficient numerical scheme to compute steep gravity waves in water of shallow uniform depth is described. The problem is formulated as a system of integrodifferential equations for the free surface. A numerical procedure based on Newton's iterations is devised to solve these equations. Solutions of high accuracy for depth as small as 1/120 of a wavelength are presented. Numerical confirmation is obtained for the existence of maxima of the potential and kinetic energies of the waves as functions of the steepness. © 1979 American Institute of Physics.