Two-dimensional internal gravity waves generated by an oscillating circle in a density stratified fluid

Abstract

Two-dimensional time-harmonic internal gravity waves are generated by an oscillating body in a density stratified, inviscid, and incompressible fluid. The waves are found in columns that form a St. Andrew's Cross. We will solve a hyperbolic partial differential equation for the pressure p in two dimensions using a reciprocal theorem. We obtain an explicit integral representation for the pressure, in terms of single-layer and double-layer potentials. A method is used for calculating the far-field of these potentials of an oscillating circle. Our solution is verified by comparing the results with a known solution.