Fig. 1

Variation of the reduced flow variables in the region behind the shock front in the case of isothermal flow: a radial component of fluid velocity \(\dfrac{u}{u_{n}}\), b azimuthal component of fluid velocity \(\dfrac{v}{v_{n}}\), c axial component of fluid velocity \(\dfrac{w}{w_{n}}\), d density (pressure) \(\dfrac{\rho }{\rho _{n}}\) \(\left( =\dfrac{p}{p_{n}}\right)\), e azimuthal magnetic field \(\dfrac{h}{h_{n}}\), f non-dimensional azimuthal component of vorticity vector \(l_{\theta }\), g non-dimensional axial component of vorticity vector \(l_{z}\): 1. \(M_{A}^{-2}=0\), \(\gamma = \dfrac{4}{3}\), \(\dfrac{\sigma }{i} =1\); 2. \(M_{A}^{-2} = 0\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1\); 3. \(M_{A}^{-2} = 0.01\), \(\gamma =\dfrac{4}{3}\), \(\dfrac{\sigma }{i}=1\); 4. \(M_{A}^{-2}= 0.01\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1\); 5. \(M_{A}^{-2} = 0.1\), \(\gamma = \dfrac{4}{3}\), \(\dfrac{\sigma }{i} =1\); 6. \(M_{A}^{-2}= 0.1\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1\); 7. \(M_{A}^{-2} = 0\), \(\gamma = \dfrac{4}{3}\), \(\dfrac{\sigma }{i} =1.5\); 8. \(M_{A}^{-2} = 0\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1.5\); 9. \(M_{A}^{-2} = 0.01\), \(\gamma = \dfrac{4}{3}\), \(\dfrac{\sigma }{i} =1.5\); 10. \(M_{A}^{-2} = 0.01\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1.5\); 11. \(M_{A}^{-2} = 0.1\), \(\gamma = \dfrac{4}{3}\), \(\dfrac{\sigma }{i} =1.5\); 12. \(M_{A}^{-2}=0.1\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1.5\)