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Multilayer shallow water equations with complete Coriolis force. Part 2.Linear plane waves

Published online by Cambridge University Press:  25 November 2011

Andrew L. Stewart  and
Paul J. Dellar
Andrew L. Stewart
Affiliation:
OCIAM, Mathematical Institute, 24–29 St Giles’, Oxford OX1 3LB, UK
Paul J. Dellar*
Affiliation:
OCIAM, Mathematical Institute, 24–29 St Giles’, Oxford OX1 3LB, UK
*
†Email address for correspondence: dellar@maths.ox.ac.uk
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Abstract

We investigate the behaviour of linear plane waves in multilayer shallow water equations that include a complete treatment of the Coriolis force. These equations improve upon the conventional shallow water equations, based on the traditional approximation, that include only the part of the Coriolis force due to the locally vertical component of the rotation vector. Including the complete Coriolis force leads to dramatic changes in the structure of long linear plane waves. It allows subinertial waves to exist with frequencies below the inertial frequency, the minimum frequency for which waves exist under the traditional approximation. These subinertial waves are characterized by a distinguished limit in which the horizontal pressure gradient becomes comparable to the upwellings and downwellings driven by the non-traditional Coriolis term in the vertical momentum equation. The subinertial waves connect wave modes that remain separate in the conventional multilayer shallow water equations, such as the surface and internal waves in a two-layer system. Eastward-propagating surface waves in a two-layer system connect with westward-propagating internal waves, and vice versa, via the long subinertial waves. The long subinertial waves cannot be classified as either surface or internal waves, due to the phase difference between the disturbances to the interfaces in these waves.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Waves in rotating fluids

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Papers
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Journal of Fluid Mechanics , Volume 690 , 10 January 2012 , pp. 16 - 50
Copyright
Copyright © Cambridge University Press 2011

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