Internal Gravity Waves and Hyperbolic Boundary-value Problems†

Talk Abstract Three-dimensional time-harmonic internal gravity waves are generated by oscillating a bounded object in an unbounded stratified fluid. Energy is found in conical wave beams. The problem is to calculate the wave fields for an object of arbitrary shape. It can be formulated as a hyperbolic boundary-value problem. The following aspects are discussed: reduction to boundary integral equations; single-layer and double-layer potentials; estimation of far fields and radiation conditions. The problem is complicated because the group and phase velocities are orthogonal. In addition, singular boundary integrals arise: their integrands are infinite along a certain curve (not just at a point) on the boundary, and this happens even when the field point is off the boundary (but within one of the conical wave beams).