Hydromagnetic cylindrical shock in self-gravitating gas (Q801776)

The Chisnell-Chester-Whitham method [\textit{R. F. Chisnell}, Proc. R. Soc. Lond., Ser. A. 232, 350-370 (1955; Zbl 0068.192); \textit{W. Chester}, Philos Mag., VII. Ser. 45, 1293-1301 (1954; Zbl 0057.186) and \textit{G. B. Whitham}, J. Fluid Mech. 4, 337-360 (1958; Zbl 0081.415)] has been used to study the propagation of diverging hydromagnetic cylindrical shock through an infinitely electrically conducting self-gravitating gas having an initial density distribution \(\rho_ 0=\rho 'r^{-w}\), where \(\rho'\) is the density at the axis of symmetry and w is a constant, simultaneously for the two cases, viz.: (i) when the shock is weak and (ii) when it is strong. The magnetic field is taken to be axial and initially of constant strength. Analytical relations for shock velocity and shock strength have been obtained. The expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived.