The F-14 Tomcat in photo at the right has generated a condensation cloud as it does a transonic flyby. It is frequently stated that such condensation illustrates the region of supersonic flow or sometimes the shock waves generated in the transonic regime. While the general pattern is indeed similar to that seen in many transonic flows, there is nothing in the physics which would suggest that the region of condensation must be coincident with the region of supersonic flow.
A more sophisticated view is that this has nothing ( directly ) to do with the occurrence of supersonic flow or shock waves. Rather, it is an illustration of the Prandtl-Glauert singularity discussed in most classes on compressible flow.
Near Mach 1, the Prandtl-Glauert singularity has amplified all pressure perturbations. As a result, the regions of expansion ( low pressure ) above the wings and cockpit correspond to much lower pressures than we would expect in an incompressible flow. As in other condensation problems, the lowered bulk pressure results in a lowering of the temperature causing condensation of the ambient water vapor.
Condensation caused by the Prandtl-Glauert singularity can be seen in steady level flight usually at low altitude under humid conditions. This contrasts with the situations associated with lift and vortex generated condensation where large accelerations (due to maneuvers) are required.
The characteristic shape of the cloud can also be used to distinguish this type of condensation from ordinary low-subsonic condensation.
A few more examples of Prandtl-Glauert singularities are found at the following links:
More images of "Prandtl-Glauert clouds" are found at:
I'm not sure about the origin of this photo. Günter Schnerr at the Universität Karlsruhe was kind enough to give me a copy back in the early 1990's. Click on the picture for a larger (83 Kb) image.
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