For subsonic compressible flows, it is sometimes possible to model the flow by applying a correction factor to the answers derived from incompressible calculations or modelling  for example, the GlauertPrandtl rule
a _{c} / a_{i} ~ 1/sqrt(1  M ^{2})
(a _{c} is compressible lift curve slope, a_{i} is the incompressible lift curve slope, and M is the Mach number).
For many other flows, their nature is qualitatively different to subsonic flows. A flow where the local Mach number reaches or exceeds 1 will usually contain shock waves. A shock is a discontinuous change in the velocity, pressure and temperature in a flow. Shocks form because information about conditions downstream of a point of sonic or supersonic flow can not propgate back upstream past the sonic point.
The behaviour of a fluid changes radically as it starts to move above the speed of sound (in that fluid). For example, in subsonic flow, a stream tube in an accelerating flow contracts. But in a supersonic flow, a stream tube in an accelerating flow expands.
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