Fundamental Solutions of Source and Vortex in a Two Dimensional Stratified Shear Flow

Abstract

Fundamental solutions of a point source and a point vortex in a two-dimensional stratified shear flow are presented. The flow has the velocity increasing exponentially with y and the density decreasing exponentially with y. The Euler equations are linearlized for small disturbances to the flow, and the method of Fourier transform is used to derive the solutions. Two types of solutions are obtained according to the magnitude of buoyancy effect; one is wavy form solution for large buoyancy and the other is non-wavy one for small buoyancy. For appropriate combination of source and vortex in a large buoyancy, the solution shows streamlines like lee waves.