Long Nonlinear Surface Waves in the Presence of a Variable Current

摘要: We investigate the eigenvalue problem governing propagation of long nonlinear surface waves when there is a current  beneath surface, y being vertical coordinate. The amplitude such evolves according to KdV equation and it was proved by Burns [1] that their speed propagation c is no critical layer (i.e., c lies outside range of ). If, however, nonlinear, result does not necessarily apply because phase change linear theory then vanishes. In this paper, we consider specific velocity profiles determine c as function Froude number for modes with layers. Such do always exist, case asymptotic suction profile  being notable example. find, singular can be obtained boundary Falkner–Skan similarity type, including Blasius case. These other examples are treated examine solutions Rayleigh gain insight about wave limit solutions.