非线性薛定谔流中的斜向空间色散shock waves
Oblique spatial dispersive shock waves in nonlinear Schrödinger flows
摘要：
在色散介质中，流体动力学奇异性通过称为色散激波（DSW）的相干波列来解决。在一维介质中，只有动态扩展的时间DSW才是可能的。二维介质中固有的额外自由度允许产生表现出空间扩展的与时间无关的DSW。利用Whitham调制理论构造了一类非线性薛定谔边值问题的空间斜激波，即经典介质中斜激波的色散模拟。自相似的，简单的波的调制方程的解决方案产生DSW的方向和上游/下游流场之间的关系。时间相关的数值模拟表明，对流或绝对不稳定性的倾斜DSW超声速流障碍。对流不稳定的结果在一个有效的稳定DSW。
英文摘要：
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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