Resonant Standing Waves on Water of Uniform Depth

Resonant standing waves on finite depth water are obtained analytically and numerically. The analytical solutions are determined to fifth order which is the minimum order to investigate harmonic resonance. Three different wave profiles are obtained for a given parameter of A₁₁, where A₁₁ is an expansion coefficient of the fundamental mode. We have found an interesting fact that the depth dependence of one of the fourth order coefficients is qualitatively different from that of the other coefficients for relatively deep water. We have furthermore obtained the analytical solution which explains the fact. A new method to calculate standing waves of large amplitude on finite depth water is also presented.