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arXiv · 1608.02632

Oblique spatial dispersive shock waves in nonlinear Schrödinger flows

M. A. Hoefer·G. A. El·A. M. Kamchatnov
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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.

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M. A. Hoefer, G. A. El, A. M. Kamchatnov. 2016-08-08. Oblique spatial dispersive shock waves in nonlinear Schrödinger flows. https://doi.org/10.1137/16m108882x

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