Oblique spatial dispersive shock waves in nonlinear Schrödinger flows

Mark Hoefer, Gennady El, Anatoly Kamchatnov

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1352–1374
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume77
Early online date17 Aug 2017
DOIs
Publication statusE-pub ahead of print - 17 Aug 2017

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