Interfacial waves and hydraulic falls: Some applications to atmospheric flows in the lee of mountains

Abstract

Two dimensional flow of a layer of constant density fluid over arbitrary topography, beneath a compressible, isothermal and stationary fluid is considered. Both downstream wave and critical flow solutions are obtained using a boundary integral formulation which is solved numerically by Newton's method. The resulting solutions are compared against waves produced behind similar obstacles in which the compressible upper layer is absent (single layer flow) and against the predictions of a linearised theory. The limiting waves predicted by the full non-linear equations are contrasted with those predicted by the forced Korteweg-de Vries theory. In particular, it is shown that at some parameter values a multiplicity of solutions exists in the full nonlinear theory.