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Double criticality and the two-way Boussinesq equation in stratifed shallow water hydrodynamics

Bridges, TJ and Ratliff, DJ (2016) Double criticality and the two-way Boussinesq equation in stratifed shallow water hydrodynamics Physics of Fluids, 28 (6), 062103.

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Abstract

Double criticality and its nonlinear implications are considered for stratified N–layer shallow water flows with N = 1,  2,  3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector and one generalized eigenvector) and semi-simple (two independent eigenvectors). Using a multiple scales argument, dictated by the type of singularity, it is shown that the weakly nonlinear problem near double criticality is governed by a two-way Boussinesq equation (non-semisimple case) and a coupled Korteweg-de Vries equation (semisimple case). Parameter values and reduced equations are constructed for the examples of two-layer and three-layer stratified shallow water hydrodynamics.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bridges, TJUNSPECIFIEDUNSPECIFIED
Ratliff, DJUNSPECIFIEDUNSPECIFIED
Date : 2 June 2016
Identification Number : 10.1063/1.4952714
Copyright Disclaimer : Copyright 2016 AIP Publishing. This is the author's accepted version.
Depositing User : Symplectic Elements
Date Deposited : 29 Jun 2016 16:29
Last Modified : 29 Jun 2016 16:29
URI: http://epubs.surrey.ac.uk/id/eprint/811077

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