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A multi-layer model for nonlinear internal wave propagation in shallow water

Published online by Cambridge University Press:  09 February 2012

Philip L.-F. Liu  and
Xiaoming Wang
Philip L.-F. Liu*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan 32001, Taiwan
Xiaoming Wang
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA GNS Science, Wairakei 3377, New Zealand
*
†Email address for correspondence: Philip.liu@cornell.edu
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Abstract

In this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an -layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 341 - 365
Copyright
Copyright © Cambridge University Press 2012

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