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

Bridges, Thomas J. and Ratliff, Daniel (2016) Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics. Physics of Fluids, 28 (6). 062103. ISSN 1070-6631

[img]
Preview
Text
r_Doublecriticality_PoF.pdf - Accepted Version

Download (535kB) | Preview
Official URL: https://doi.org/10.1063/1.4952714

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: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 17 Aug 2020 11:19
Last Modified: 17 Aug 2020 11:30
URI: http://nrl.northumbria.ac.uk/id/eprint/44106

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics