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Instability and focusing of internal tides in the deep ocean

Published online by Cambridge University Press:  24 September 2007

OLIVER BÜHLER  and
CAROLINE J. MULLER
OLIVER BÜHLER
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
CAROLINE J. MULLER*
Affiliation:
Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Author to whom correspondence should be addressed.
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Abstract

The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.

As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above.

For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.

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Papers
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Journal of Fluid Mechanics , Volume 588 , 10 October 2007 , pp. 1 - 28
Copyright
Copyright © Cambridge University Press 2007

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