Mach number ($\mathcal{M}$)

The Mach number is the ratio of flow speed to local sound speed.

The radial Mach number is the source velocity projected toward the observer, divided by the sound speed. It enters the moving-surface retarded Jacobian through $d|x-y(\tau )|/d\tau =-\hat{r}\cdot v$. The sign is directional: a source moving toward the observer has positive $M_r$ and compressed arrival times.

A subsonic flow has Mach number less than one, so its speed is below the local sound speed.

A supersonic flow has Mach number greater than one, so the flow speed exceeds the local sound speed.