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Prandtl–Glauert singularity
The Prandtl–Glauert singularity is the prediction by the Prandtl–Glauert transformation that infinite pressures would be experienced by an aircraft as it approaches the speed of sound. Because it is invalid to apply the transformation at these speeds, the predicted singularity does not emerge. This is related to the early 20th century misconception of the impenetrability of the sound barrier.
== Reasons of invalidity around Mach 1 ==
The Prandtl-Glauert transformation assumes linearity (i.e. a small change will have a small effect that is proportional to its size). This assumption becomes inaccurate at high Mach numbers and is entirely invalid in places where the flow reaches supersonic speeds, since sonic shock waves are instantaneous (and thus very non-linear) changes in the flow. 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. As the flow approaches sonic speed, the nonlinear phenomena dominate within the flow, which this transformation completely ignores for the sake of simplicity.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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