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Fig. 2 | SpringerPlus

Fig. 2

From: Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density

Fig. 2

Variation of the reduced flow variables in the region behind the shock front in the case of adiabatic 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 \(\dfrac{\rho }{\rho _{n}}\), e pressure \(\dfrac{p}{p_{n}}\), f azimuthal magnetic field \(\dfrac{h}{h_{n}}\), g non-dimensional azimuthal component of vorticity vector \(l_{\theta }\), h 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. \(M_{A}^{-2} = 0.1\), \(\gamma = \dfrac{5}{3}\), \(\dfrac{\sigma }{i} =1.5\)

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