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Convective instability of stably stratified water in the ocean

Published online by Cambridge University Press:  12 April 2006

S. Leibovich
S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
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Abstract

A recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification. The interaction leads to a convective instability even when the density stratification is statically stable. An unspecified random surface wave field is permitted provided that it is statistically stationary.

The instability can be traced to torques produced by variations of a ‘vortex force’. Non-diffusive instabilities produced by this mechanism in water of infinite depth are explored in detail for arbitrary distributions of the destabilizing force. Stability is determined by an eigenvalue problem formally identical to that determining normal modes of infinitesimal internal waves in fluid with a density profile that is not monotone and thereby has a statically unstable region. Some tentative remarks are offered about the problem when dissipation is allowed.

Application of the present theory to Langmuir circulations is discussed. Also, according to the present theory, internal wave propagation should be modified by the vortex force arising from the interaction between the surface waves and the current.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 3 , 27 September 1977 , pp. 561 - 581
Copyright
© 1977 Cambridge University Press

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