Expansion shock waves in regularized shallow-water theory

El, Gennady, Hoefer, Mark and Shearer, Michael (2016) Expansion shock waves in regularized shallow-water theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2189). p. 20160141. ISSN 1364-5021

AAM_el et al_2016_PRSA_Expansion shock.pdf - Accepted Version

Download (8MB) | Preview
Official URL: https://doi.org/10.1098/rspa.2016.0141


We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

Item Type: Article
Uncontrolled Keywords: Lax entropy condition, non-local dispersion, Benjamin–Bona–Mahony equation, Boussinesq equations
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 03 Dec 2018 11:58
Last Modified: 01 Aug 2021 11:20
URI: http://nrl.northumbria.ac.uk/id/eprint/37026

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics