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Scattering of gravity waves by potential vorticity in a shallow-water fluid

Published online by Cambridge University Press:  08 October 2010

MARSHALL L. WARD  and
WILLIAM K. DEWAR
MARSHALL L. WARD*
Affiliation:
Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306, USA
WILLIAM K. DEWAR
Affiliation:
Department of Oceanography, Florida State University, Tallahassee, FL 32306, USA
*
†Present address: Research School of Earth Sciences, Australian National University, Canberra, ACT 0200 Australia. Email address for correspondence: [email protected]
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Abstract

The influence of a geostrophically balanced or potential vorticity (PV) containing background flow on the propagation of a coherent gravity wave is examined in a rotating shallow-water model. Over inertial time scales, we find that the gravity wave energy is scattered into other modes of similar wavelength, but with different directions of propagation. We attribute this response to nonlinear resonant interactions between the PV and gravity wave modes, despite the absence of any exchange of energy between the two, and show that the response is consistent with resonant triad theory. We first consider the scattering of a gravity wave mode due to a single PV mode, and compare the theoretical response to numerical solutions. This is followed by consideration of the propagation of a coherent gravity mode through a turbulent PV background. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.

JFM classification

Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Quasi-geostrophic flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 478 - 506
Copyright
Copyright © Cambridge University Press 2010

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