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Equatorially trapped nonlinear water waves in a $\unicode[STIX]{x1D6FD}$-plane approximation with centripetal forces

Published online by Cambridge University Press:  31 August 2016

David Henry
David Henry*
Affiliation:
Department of Applied Mathematics, University College Cork, Cork, Ireland
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we present an exact and explicit nonlinear solution of a $\unicode[STIX]{x1D6FD}$-plane approximation to the governing equations which retains all Coriolis terms. The solution represents an equatorially trapped wave propagating in the presence of a constant underlying background current. In particular, we show that retention of the (relatively) small-scale centripetal forces in the governing equations enables us to admit currents of any physically plausible magnitude in the background flow.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , R1
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Copyright
© 2016 Cambridge University Press 

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