Instability of strong regular reflection and counterexamples to the detachment criterion

Details Instability of strong regular reflection and counterexamples to the detachment criterion Instability of strong regular reflection and counterexamples to the detachment criterion

2009-08-02

arxiv.org/abs/0908.0106v2

Physics

Mathematical Physics

Formatting corrected

Scientific paper

We consider a particular instance of reflection of shock waves in self-similar compressible flow. We prove that local self-similar regular reflection (RR) cannot always be extended into a global flow. Therefore the detachment criterion is not universally correct. More precisely, consider the following "angle condition": the tangent of the strong-type reflected shock meets the opposite wall at a sharp or right downstream side angle. In cases where the condition is violated and the weak-type reflected shock is transonic, we show that global RR does not exist. Combined with earlier work we have shown that none of the classical criteria for RR-MR transition is universally correct. A new criterion is proposed. Moreover, we have shown that strong-type RR is unstable, in the sense that global RR cannot persist under perturbations to one side. This yields a definite answer to the weak-strong problem because earlier work shows stability of weak RR in the same sense.

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