Closed Form Solution for a Point Force in a Rotating Stratified Fluid

Abstract

The motion generated by an oscillatory point force in an inviscid incompressible rotating stratified fluid is studied, taking into account the effect of stratification on the inertia terms in the equations of motion. The solutions are obtained in closed form using Fourier transforms. The motion is axisymmetric (or not) according as the force acts along (or perpendicular to) the axis of rotation of the fluid. In the hyperbolic case, the motion is confined to the inner region of a cone with vertex at the origin. The solution when there is no rotation - no stratification - neither rotation nor stratification, is deduced and each case is found to differ from the case of rotating stratified fluid in many respects. The solution for a steady force is also deduced in the limit.