Oblique Spatial Dispersive Shock Waves in Nonlinear Schrödinger Flows

Hoefer, Mark, El, Gennady and Kamchatnov, Anatoly (2017) Oblique Spatial Dispersive Shock Waves in Nonlinear Schrödinger Flows. SIAM Journal on Applied Mathematics, 77 (4). pp. 1352-1374. ISSN 0036-1399

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Official URL: http://dx.doi.org/10.1137/16M108882X

Abstract

In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schrödinger boundary value problems. Self-similar, simple wave solutions of the modulation equations yield relations between the DSW's orientation and the upstream/downstream flow fields. Time dependent numerical simulations demonstrate a convective or absolute instability of oblique DSWs in supersonic flow over obstacles. The convective instability results in an effective stabilization of the DSW.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Paul Burns
Date Deposited: 16 Nov 2018 17:28
Last Modified: 11 Oct 2019 18:30
URI: http://nrl.northumbria.ac.uk/id/eprint/36765

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