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

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.

Type
Rapids
Copyright
© 2016 Cambridge University Press 

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