Commun. Comput. Phys., 12 (2012), pp. 1461-1481.


Numerical Simulation of a Weakly Nonlinear Model for Internal Waves

Robyn Canning Gregory 1, David P. Nicholls 1*

1 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA.

Received 14 August 2011; Accepted (in revised version) 6 January 2012
Available online 8 May 2012
doi:10.4208/cicp.140811.060112a

Abstract

Internal waves arise in a wide array of oceanographic problems of both theoretical and engineering interest. In this contribution we present a new model, valid in the weakly nonlinear regime, for the propagation of disturbances along the interface between two ideal fluid layers of infinite extent and different densities. Additionally, we present a novel high-order/spectral algorithm for its accurate and stable simulation. Numerical validation results and simulations of wave-packet evolution are provided.

AMS subject classifications: 76B07, 76B15, 76B55, 65M70

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Key words: Internal waves, weakly nonlinear waves, high-order spectral methods, Dirichlet Neumann operators, surface formulation.

*Corresponding author.
Email: rcanni2@uic.edu (R. C. Gregory), nicholls@math.uic.edu (D. P. Nicholls)
 

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