On the three-dimensional internal waves excited by topography in the flow of a stratified fluid

Abstract

A numerical study of the three-dimensional internal waves excited by topography in the flow of a stratified fluid is described. In the resonant flow of a nearly two-layer fluid, it is found that the time-development of the nonlinearly excited waves agrees qualitatively with the solution of the forced KP equation or the forced extended KP equation. In this case, the upstream-advancing solitary waves become asymptotically straight crested because of abnormal reflection at the sidewall similar to Mach reflection. The same phenomenon also occurs in the subcritical flow of a nearly two-layer fluid. However, in the subcritical flow of a linearly stratified Boussinesq fluid, the two-dimensionalization of the upstream waves can be interpreted as the separation of the lateral modes due to the differences in the group velocity of the linear wave, although this does not mean in general that the generation of upstream waves is describable by the linearized equation.