In fluid dynamics, a moving shock is a shock wave that is traveling through a fluid (often gaseous) medium with a velocity relative to the velocity of the fluid already making up the medium.[1] As such, the normal shock relations require modification to calculate the properties before and after the moving shock. A knowledge of moving shocks is important for studying the phenomena surrounding detonation, among other applications.
To derive the theoretical equations for a moving shock, one may start by denoting the region in front of the shock as subscript 1, with the subscript 2 defining the region behind the shock. This is shown in the figure, with the shock wave propagating to the right. The speed of the shock wave relative to the gas is W, making the total velocity equal to u1 + W. Additionally, the pressure is denoted by p and the local speed of sound by a.
Next, suppose a reference frame is then fixed to the shock so it appears stationary as the gas in regions 1 and 2 move with a velocity relative to it