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Title: The steady-state form of large-amplitude internal solitary waves
Authors: King, Stuart Edward
Carr, Magda
Dritschel, David Gerard
Keywords: Internal waves
Solitary waves
Stratified flows
QA Mathematics
Issue Date: 10-Jan-2011
Citation: King , S E , Carr , M & Dritschel , D G 2011 , ' The steady-state form of large-amplitude internal solitary waves ' Journal of Fluid Mechanics , vol 666 , pp. 477-505 . , 10.1017/S0022112010004301
Abstract: A new numerical scheme for obtaining the steady-state form of an internal solitary wave of large amplitude is presented. A stratified inviscid two-dimensional fluid under the Boussinesq approximation flowing between horizontal rigid boundaries is considered. The stratification is stable, and buoyancy is continuously differentiable throughout the domain of the flow. Solutions are obtained by tracing the buoyancy frequency along streamlines from the undisturbed far field. From this the vorticity field can be constructed and the streamfunction may then be obtained by inversion of Laplace's operator. The scheme is presented as an iterative solver, where the inversion of Laplace's operator is performed spectrally. The solutions agree well with previous results for stratification in which the buoyancy frequency is a discontinuous function. The new numerical scheme allows significantly larger amplitude waves to be computed than have been presented before and it is shown that waves with Richardson numbers as low as 0.062 can be computed straightforwardly. The method is also extended to deal in a novel way with closed streamlines when they occur in the domain. The new solutions are tested in independent fully nonlinear time-dependent simulations and are verified to be steady. Waves with regions of recirculation are also discussed.
Version: Postprint
Status: Peer reviewed
ISSN: 0022-1120
Type: Journal article
Rights: This is the author's version of this article. The published version (c)Cambridge University Press is available from
Appears in Collections:University of St Andrews Research
Mathematics & Statistics Research
Applied Mathematics Research
Scottish Oceans Institute Research

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