Plane and cylindrical hydromagnetic shock waves
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 investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial \((H_ 0)\) and variable azimuthal \((H_{\theta_ 0}=r^{1/2}H_ 0)\) components, simultaneously for both weak and strong cases. Assuming an initial density distribution \(\rho_ 0=\rho 'r^ w\), where \(\rho\) ' is the density at the plane/axis of symmetry and w is a constant, the analytical expressions 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 for both cases.
scientific article; zbMATH DE number 3878609