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On the surface, the Prandtl--Glauert singularity explains this, just as it explains the formation of a single "ring" of condensate about aircraft going transonic. The "cloud" here is sometimes called a vapor cone for its shape (conical -- a cone) and the material out of which it is made (water vapor). The effects of the reduced air pressure "inside" the cone of high pressure that is the supersonic shock wave generate the cloud. This is generally true, though there is still some debate over the specific mechanisms involved in producing the Prandtl-Glauert singularity. But, as it turns out, there is almost always a catch to things like this. The F-4 may not have been transonic. We sometimes see condensate forming around the wings of aircraft, depending on conditions and the airspeed of the vehicle, even though the plane is subsonic. Certainly higher airspeed promotes the creation of areas of dramatically lower pressure in places like the wings. And we are aware that if pressure dramatically drops in a given situation, the air cools, which could facilitate the formation of condensation. A link is posted below to a dramatic picture of an F/A-18 going transonic. But further down in the article, you can see a pair of photos of an F-4 (taken of the "Black Bunny" back in '71) with two distinct areas where vapor is forming. Heck, even in the shot of the F/A-18, you can see a bit of vapor forming at the trailing edge of the canopy. With the F-4, the "clouds" of vapor appear at the engine inlets where they stick out from the body of the aircraft into the airstream. These vapor formations are thought to appear as a result of decompression behind compressive leading edge of the shock wave that is set up at the leading edge of the aircraft, or parts of it. This may not sit well with some, but there are shots of the B-1 a bit further down in the post, and it, too, has a vapor cloud about it. Further, this aircraft does not have transonic capability. Links can be found below to explanations of Prandtl-Glauert singularity.

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Q: In a view of transonic condensation over an F4 Phantom the condensation is in the form of two rings rather than one large cloud. How is the effect explained?
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