One-dimensional flow: plane normal shock waves
In the previous section the behaviour of gas when acting as a transmitter of waves of infinitesimal amplitude was considered and the waves were shown to travel at an (acoustic) speed of a = Jdpjdp relative to the gas, while the gas properties of pressure, density etc. varied in a continuous manner.
If a disturbance of large amplitude, e. g. a rapid pressure rise, is set up there are almost immediate physical limitations to its continuous propagation. The accelerations of individual particles required for continuous propagation cannot be sustained and a pressure front or discontinuity is built up. This pressure front is known as a shock wave which travels through the gas at a speed, always in excess of the acoustic speed, and together with the pressure jump, the density, temperature and entropy of the gas increases suddenly while the normal velocity drops.
Useful and quite adequate expressions for the change of these flow properties across the shock can be obtained by assuming that the shock front is of zero thickness. In fact the shock wave is of finite thickness being a few molecular mean free path lengths in magnitude, the number depending on the initial gas conditions and the intensity of the shock.