Critical Mach numbers in classical magnetohydrodynamics

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Abstract
We use stationary point analysis to compute generalized critical Mach numbers for finite amplitude fast and slow shocks in classical MHD fluids. We pay particular attention to the case where the resistive and thermal conduction dissipation scale lengths are comparable and much larger than the viscous scale lengths. With both resistivity and thermal conduction, the critical Mach number at which viscosity must be invoked is determined by the condition that the downstream flow speed equal the isothermal sound speed. We also show that resistivity and thermal conduction can provide convergent stationary point solutions for nearly all slow shocks, except perhaps switch‐off shocks.