On Certain Properties of Hydromagnetic Shocks

Proofs of four basic properties of stationary, planar, nonrelativistic hydromagnetic shocks are presented. These properties are: $({\mathcal{P}}_1)$ the specific entropy behind a hydromagnetic shock exceeds that ahead, if and only if, the shock is compressive; $({\mathcal{P}}_2)$ the specific entropy behind a compressive shock varies in the same sense as the mass flux; $({\mathcal{P}}_3)$ in the region behind (compressive) fast shocks, the fast disturbance speed is greater than the normally directed fluid velocity relative to the shock; $({\mathcal{P}}_4)$ in the region behind (compressive) slow shocks, the slow disturbance speed may be less than, equal to, or greater than the normally directed fluid velocity relative to the shock. The equality holds when the specific entropy and the mass flux assume their maximum values. In these statements the state in front is assumed fixed and attention is focused on the variation of the state behind with an appropriate shock strength parameter. The proof of ${\mathcal{P}}_1$ is designed especially to cover the case of the slow shock where the dependence of the state behind on the ``natural'' shock‐strength parameters is nonmonotonic. Our proofs of ${\mathcal{P}}_3$ and ${\mathcal{P}}_4$ require the medium to be a polytropic ideal gas; however, a less stringent assumption suffices for ${\mathcal{P}}_1$ and ${\mathcal{P}}_2$ .