On the Propagation of Shock Waves

For a strong shock wave propagating into an expanding channel, an improved characteristic method is re-explained in a slightly different manner. A new physical quantity (labelled χ) is introduced for the method. The quantity indicates a magnitude of damping (χ>0) or growing (χ<0) of the shock wave. Then, the positive (minor) characteristic equation is converted to the major characteristic one along the particle path line. By simultaneous using of this characteristic equation, the negative characteristic one and Brinkley-Kirkwood's (1947) method for the shock propagation, the entire flow field is determined as a function of χ. The solutions are in good agreement with similarity ones. Accordingly, this method is applied to the propagation of cylindrical shock waves under the actions of the differential rotation of gas itself, the gravitational field of the other mass and the circular magnetic field, and the governing equations are formulated. Furthermore, various methods are briefly outlined and compared with the above method. Especially, for Chisnell's method it is found that the propagation of a shock wave can be solved analytically under the action of gravity. The solution brings out the clear perspective of the variation of the shock strength.