2023/09/20 by Jonathan Granot, Granot, Jonathan, Michael Rabinovich +1
Physics and Astronomy · Engineering · #Astrophysics and Star Formation Studies #Computational Fluid Dynamics and Aerodynamics #Astrophysical Phenomena and Observations
paper · pdf · doi:10.48550/arxiv.2309.11293
Shock wave reflection from a rigid wall has been thoroughly studied in the Newtonian limit, simplifying the problem by analyzing it in a steady-state frame, S', where the point P of the shock's intersection with the wall is at rest. However, a "super-luminal" regime emerges when the velocity of point P (vp) exceeds the speed of light (vp>c), where no steady-state frame S' exists. It occurs predominantly in the relativistic regime, relevant in astrophysics, where it encompasses nearly all of the shock incidence angles. To study this regime, we introduce a new approach. We formulate integral conservation laws in the lab frame S (where the unshocked fluid is at rest) for regular reflection (RR), using two methods: a. fixed volume analysis and b. fixed fluid analysis. We show the equivalence between the two methods, and also to the steady-state oblique shock jump conditions in frame S' in the sub-luminal regime (vp