Resonant Standing Waves on Water of Uniform Depth

Abstract

Resonant standing waves on finite depth water are obtained analytically andnumerically. The analytical solutions are determined to fifth orderwhich is the minimum order to investigate harmonic resonance.Three different wave profiles are obtained for a given parameter ofA₁₁, where A₁₁ is an expansion coefficient of the fundamental mode.We have found an interesting fact that the depth dependence of one ofthe fourth order coefficients is qualitatively different fromthat of the other coefficients for relatively deep water.We have furthermore obtained the analytical solution which explains the fact.A new method to calculatestanding waves of large amplitude on finite depth water is also presented.