Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

Abstract

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.

Appendix: MHD shock jump relations for ideal gas (Whitham 1958; Anand 2000)

where $a_{o} = \sqrt{\gamma p_{o} / \rho _{o}}$ and $b_{o} = \sqrt{\mu H_{o}^{2} / \rho _{o}}$.

Jump relations for WSWMF

Jump relations for WSSMF

Jump relations for SSWMF

where $\chi ' = \frac{\gamma ( \xi - 1 )}{\xi}$, $A' = \frac{\gamma ( \xi - 1 )}{4\xi} [ ( \gamma - 1 )( \xi - 1 )^{2} - 2\{ ( 2 - \gamma)\xi + \gamma\} ]$.

Jump relations for SSSMF

where $\chi = \frac{\gamma ( \gamma - 1 )( \xi - 1 )^{3}}{2\xi \{ ( 2 - \gamma )\xi + \gamma \}}$, $A = \frac{4}{( \gamma - 1 )( \xi - 1 )^{2}} - \frac{2}{( 2 - \gamma )\xi + \gamma}$.