Internal Gravity Wave Propagation through a Sharp Thermocline.
DENVER RESEARCH INST COLO DIV OF MATHEMATICAL SCIENCES
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This paper is concerned with the investigation of internal gravity wave propagation in a deep ocean where the waves are produced by a moving source. This is all in the presence of a sharp thermocline a region over which there is a rapid change in temperature. The model studied is described by a linearization of the fluid equations brought about by assuming that the internal waves are small amplitude perturbations on a prescribed inviscid incompressible ambient state. The thermocline is modeled by an interface problem where a jump discontinuity exists in an otherwise constant Brunt-Vaisala frequency which is a measure of the natural frequency of fluid oscillations under the restoring effects of gravity. An exact integral representation is obtained for the solution via FOURIER transforms and elimination. Integrals representing incident, reflected and transmitted waves are then approximated using multi-dimensional stationary phase and steepest descent. The phenomena of transition radiation along with lateral wave propagation from the interface back to the region of disturbance are also studied. We find transition radiation but no lateral wave. Machinery is brought to bear on two particular examples, a source moving with a vertical trajectory and an oscillating stationary source. For this later source we offer a new interpretation of some experimental results. Author
- Physical and Dynamic Oceanography