Calculation of forced, nonlinear water waves in a square container (Q1324728)

An investigation is presented of the evolution near resonance of three- dimensional water waves in a square container driven in two-dimensional, horizontal, sinusoidal motion parallel to a wall. Since perturbation methods fail near resonance, it is shown how particular periodic solutions of the nonlinear governing equations can be obtained directly from the nonlinear boundary value problem by a collocation method in Fourier space. Calculations of the linear stability and the nonlinear time evolution of solutions are presented also.