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Solutions of barotropic trapped waves around seamounts

Published online by Cambridge University Press:  08 September 2010

LUIS ZAVALA SANSÓN
LUIS ZAVALA SANSÓN*
Affiliation:
Department of Physical Oceanography, CICESE, Carretera Ensenada-Tijuana 3918, 22860 Ensenada, Baja California, Mexico
*
†Email address for correspondence: lzavala@cicese.mx
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Abstract

In this paper, solutions of free, barotropic waves around axisymmetric seamounts are derived. Even though this type of oscillation has been studied before, we revisit this problem for two main reasons: (i) the linear, barotropic, shallow-water equations with a rigid lid are now solved with no further approximations, in contrast with previous studies; (ii) the solutions are applied to a wide family of seamounts with profiles proportional to exp(rs), with r being the radial distance from the centre of the mountain and s any positive real number. (Most previous works are restricted to the special case s = 2.) The resulting dispersion relation possesses a remarkable simplicity that reveals a number of wave characteristics, for instance, the discrete wave frequencies and the angular phase speed of the waves around the seamount are easily derived as a function of the seamount shape. By varying the shape parameter one can study trapped waves around flat-topped seamounts or guyots (s > 2) or sharp, cone-shaped topographies (s < 2).

JFM classification

Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 32 - 44
Copyright
Copyright © Cambridge University Press 2010

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References

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