Mach waves and shock waves in two-dimensional flow

A small deflection in supersonic flow always takes place in such a fashion that the flow properties are uniform along a front inclined to the flow direction, and their only change is in the direction normal to the front. This front is known as a wave and for small flow changes it sets itself up at the Mach angle (p) appropriate to the upstream flow conditions.

For finite positive or compressive flow deflections, that is when the downstream pressure is much greater than that upstream, the (shock) wave angle is greater than the Mach angle and characteristic changes in the flow occur (see Section 6.4). For finite negative or expansive flow deflections where the downstream pressure is less, the turning power of a single wave is insufficient and a fan of waves is set up, each inclined to the flow direction by the local Mach angle and terminating in the wave whose Mach angle is that appropriate to the downstream condition.

For small changes in supersonic flow deflection both the compression shock and expansion fan systems approach the character and geometrical properties of a Mach wave and retain only the algebraic sign of the change in pressure.