2016/08/08 by M. A. Hoefer, G. A. El, A. M. Kamchatnov
Physics and Astronomy · #nlin.PS
paper · pdf · doi:10.1137/16m108882x
published as SIAM J Appl Math, Vol 77, pp 1352-1374, 2017 · 23 pages, 7 figures
arxiv created 2016/08/08 · arxiv updated 2017/11/01
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.