Prandtl - Glauert singularity (13 pics)

The Prandtl–Glauert singularity (sometimes referred to as a "vapor cone"), is the point at which a sudden drop in air pressure occurs, and is generally accepted as the cause of the visible condensation cloud that often surrounds an aircraft traveling at transonic speeds, though there remains some debate. It is an example of a mathematical singularity in aerodynamics. One view of this phenomenon is that it exhibits the effect of compressibility and the so-called "N-wave". The N-wave is the time variant pressure profile seen by a static observer when a sonic compression wave passes. The overall three-dimensional shock wave is in the form of a cone with its apex at the supersonic aircraft. This wave follows the aircraft. The pressure profile of the wave is composed of a leading compression component (the initial upward stroke of the "N"), followed by a pressure descent forming a rarefaction of the air (the downward diagonal of the "N"), followed by a return to the normal ambient pressure (the final upward stroke of the "N"). The rarefaction may be thought of as the "rebounding" of the compression due to inertial effects.