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Internal tides and the inviscid dynamics of an oscillating ellipsoid in a stratified fluid

Published online by Cambridge University Press:  14 November 2024

Bruno Voisin Open the ORCID record for Bruno Voisin [Opens in a new window]
Bruno Voisin*
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, Université Grenoble Alpes, CNRS, Grenoble INP, 38000 Grenoble, France
*
†Email address for correspondence: [email protected]
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Abstract

A boundary integral representation is derived for the translational oscillations of a triaxial ellipsoid in a uniformly stratified fluid. The representation is of single-layer type, a distribution of sources and sinks over the surface of the ellipsoid. The added mass tensor of the ellipsoid is deduced from it and, from this tensor, the impulse response function together with the energy radiated away as internal waves. Horizontal oscillations correspond to the generation of an internal or baroclinic tide by the oscillation of the barotropic tide over ellipsoidal topography at the bottom of the stratified ocean. Such topography is unconditionally supercritical, namely of slope larger than the slope of the wave rays, irrespective of the frequency of oscillation. So far, analytical work on supercritical topographies has been limited, for the most part, to two-dimensional set-ups. Here, for the ellipsoidal seamount, the orientation of the barotropic tide and the anisotropy of the topography have their effects analysed in detail. As the height of the seamount increases, the rate of conversion of barotropic energy into baroclinic form is seen to first increase according to the square law expected for a topography of small slope, then saturate and eventually decrease.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A59
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© The Author(s), 2024. Published by Cambridge University Press

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