Magnetohydrodynamic Flow in a Shock Tube

• Published in: The Physics of fluids (1958) 1959-01, Vol.2 (1), p.62-71
• Main Author: Mitchner, M.
• Format: Article
• Language: English
• ISSN: 0031-9171; 2163-4998
• DOI: 10.1063/1.1724394

The effect of a transverse magnetic field on the motion of a perfectly conducting fluid in a shock tube is examined. A generalized form of the Riemann invariant for the continuous motion of such a fluid is combined with the conservation equations for a magnetohydrodynamic shock to obtain an exact description of the fluid motion in a shock tube in terms of arbitrary initial conditions. The fluids are assumed to have constant specific heat ratios. Qualitatively, the effect of the magnetic field is equivalent to that of a pressure, but quantitatively the effect is always greater than merely the hydrodynamic pressure equivalent of the appropriate Maxwell stress. A magnetic field in the high‐pressure region alone can produce shocks having Mach numbers for typical laboratory conditions, of the order of hundreds, and in general is in agreement with available experimental results. A magnetic field in the low‐pressure region results in weaker, but higher velocity shocks.