Generation of Internal Gravity Waves by an Oscillating Horizontal Elliptical Plate

Abstract. Time-harmonic oscillations of a horizontal plate generate internal gravity waves in an unbounded stratified fluid. A plane-wave (Fourier) decomposition is used in which waves with outgoing group velocity are selected. The pressure and the velocity in the far field are estimated in terms of the Fourier transform of the pressure jump across the plate. Explicit solutions are obtained for arbitrary prescribed motions of an elliptical plate. Energy is confined to certain wave beams, bounded by conical characteristic surfaces of the underlying hyperbolic partial differential equation; the solution itself is not axisymmetric. The details of the beam structure are complicated (because each characteristic surface has a vertical axis of symmetry, whereas the elliptical plate does not), but they emerge naturally from the asymptotic method, a method that has wider applicability. Results for analogous piston problems are also obtained; these problems arise when a piece of a rigid horizontal plane is forced to oscillate, thus generating waves above the plane.