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A regularized model for strongly nonlinear internal solitary waves

Published online by Cambridge University Press:  15 June 2009

WOOYOUNG CHOI ,
RICARDO BARROS  and
TAE-CHANG JO
WOOYOUNG CHOI*
Affiliation:
Department of Mathematical Science, Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
RICARDO BARROS
Affiliation:
Department of Mathematical Science, Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
TAE-CHANG JO
Affiliation:
Department of Mathematics, Inha University, Incheon 402-751, Korea
*
†Email address for correspondence: [email protected]
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Abstract

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 73 - 85
Copyright
Copyright © Cambridge University Press 2009

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References

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