Prandtl–Glauert singularity

It is the prediction by the Prandtl–Glauert transformation that infinite pressures would be experienced by an aircraft as it approaches the speed of sound.

Indeed, one assumption in the Prandtl–Glauert transformation is approximately constant Mach number throughout the flow, and the increasing slope in the transformation indicates that very small changes will have a very strong effect at higher Mach numbers, thus violating the assumption, which breaks down entirely at the speed of sound.

This means that the singularity featured by the transformation near the sonic speed (M=1) is not within the area of validity.

The aerodynamic forces are calculated to approach infinity at the so-called Prandtl–Glauert singularity; in reality, the aerodynamic and thermodynamic perturbations do get amplified strongly near the sonic speed, but they remain finite and a singularity does not occur.

The Prandtl–Glauert transformation is a linearized approximation of compressible, inviscid potential flow.

The Prandtl–Glauert transformation is found by linearizing the potential equations associated with compressible, inviscid flow.

The reason that observable clouds sometimes form around high speed aircraft is that humid air is entering low-pressure regions, which also reduces local density and temperature sufficiently to cause water to supersaturate around the aircraft and to condense in the air, thus creating clouds.

In the case of objects at transonic speeds, the local pressure increase happens at the shock wave location.