NONLINEAR INTERACTIONS AMONG GRAVITY SURFACE WAVES

Based on the perturbation method, a fourth order theory for nonlinear interactions among three dimensional gravity waves in water of any uniform depth is presented in this paper. Two cases are considered:(i) wave number vectors fixed, frequencies perturbed, and (ii) wave number vectors and frequencies both fixed. According to this solution, expressions of thesame order for progressive waves, short-crested waves and nonlinear interaction between wave and vertical wall are also derived.