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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’
Based on the perturbation method, a fourth order theory for nonlinear interactions among three dimensional gravity waves in water of any uniform 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. expressions of thesame order for progressive waves, short-crested waves and nonlinear interaction between wave and vertical wall are also derived ’