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Spectral Methods for Internal Waves: Indistinguishable Density Profiles and Double-humped Solitary Waves : Volume 18, Issue 3 (14/06/2011)

By Dunphy, M.

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Book Id: WPLBN0003974114
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Spectral Methods for Internal Waves: Indistinguishable Density Profiles and Double-humped Solitary Waves : Volume 18, Issue 3 (14/06/2011)  
Author: Dunphy, M.
Volume: Vol. 18, Issue 3
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Stastna, M., Subich, C., & Dunphy, M. (2011). Spectral Methods for Internal Waves: Indistinguishable Density Profiles and Double-humped Solitary Waves : Volume 18, Issue 3 (14/06/2011). Retrieved from

Description: Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada. Internal solitary waves are widely observed in both the oceans and large lakes. They can be described by a variety of mathematical theories, covering the full spectrum from first order asymptotic theory (i.e. Korteweg-de Vries, or KdV, theory), through higher order extensions of weakly nonlinear-weakly nonhydrostatic theory, to fully nonlinear-weakly nonhydrostatic theories and finally exact theory based on the Dubreil-Jacotin-Long (DJL) equation that is formally equivalent to the full set of Euler equations. We discuss how spectral and pseudospectral methods allow for the computation of novel phenomena in both approximate and exact theories. In particular we construct markedly different density profiles for which the coefficients in the KdV theory are very nearly identical. These two density profiles yield qualitatively different behaviour for both exact, or fully nonlinear, waves computed using the DJL equation and in dynamic simulations of the time dependent Euler equations. For exact, DJL, theory we compute exact solitary waves with two-scales, or so-called double-humped waves.

Spectral methods for internal waves: indistinguishable density profiles and double-humped solitary waves

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