Mach waves can be used in schlieren or shadowgraph observations to determine the local Mach number of the flow.
2.
Now, for irrotational flow the velocity is the gradient of the velocity potential, and the local Mach number components are defined as:
3.
Real choke phenomena is a function of compressibility as measured by the local Mach number within an area restriction within the centrifugal pressure stage.
4.
In the case of aircraft, the cloud is caused by stern shock wave associated with a return to subsonic flow behind the aircraft . Since the local Mach number is not uniform over the aircraft, parts of the aircraft may be supersonic while others remain subsonic a flight regime called transonic flight.
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