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Nonlinear interfacial wave formation in three dimensions

Published online by Cambridge University Press:  23 February 2015

John Grue
John Grue*
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway
*
†Email address for correspondence: johng@math.uio.no
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Abstract

A three-dimensional two-layer, fully dispersive and strongly nonlinear interfacial wave model, including the interaction with a time-varying bottom topography, is developed. The method is based on a set of integral equations. The source and dipole terms are developed in series expansions in the vertical excursions of the interface and bottom topography, obtaining explicit inversion by Fourier transform. Calculations of strongly nonlinear interfacial waves with excursions comparable to the thinner layer depth show that the quadratic approximation of the method contains the essential dynamics, while the additional cubic terms always are small. Computations confirm the onset of wave train formation driven by topography, observed in experiments (Maxworthy, J. Geophys. Res., vol. 84(C1), 1979, pp. 338–346), depending on the Froude number and the topography height. Simulations of tidally driven three-dimensional internal wave formation show the formation of two wave trains per half tidal cycle for strong forcing and one wave train for weak forcing. Waves of both backward and forward curvature are calculated.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 735 - 762
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Copyright
© 2015 Cambridge University Press 

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