The pressure field
Four deficits that add: tip vortices, leading-edge vortices, the wing's suction and the cone.
The field is the pressure round the aircraft, as four deficits that add. The cloud forms wherever the total is deep enough to take the parcel past its dew point.
Tip vortices
Each tip vortex is a Scully vortex holding part of the circulation. It leaves
the tip with a core a few per cent of the tip's chord across, and the wake
sheet rolls up into it over 0.28 AR / C_L spans (Spreiter and Sacks): within
a span in a hard pull, several in a gentle one. So the trail starts as a thread
at the tip and swells as it rolls up.
It trails along the free stream, rolls inboard to π/4 of the span and sinks under its own downwash. Its core spreads by turbulent diffusion until its pressure well is too shallow to fog. So the trail is longer for a heavier pull, a slower aircraft and moister air.
Leading-edge vortices
Each is conical, so its core pressure is the same all the way along, until it bursts. There its core swells, and the vapor fades into a ragged puff.
The wing's suction
The upper surface carries thin-airfoil theory's suction, the peak at the nose handed to the leading-edge vortex once the flow separates off a sharp edge. It is corrected for compressibility with Kármán–Tsien and simple sweep theory.
Once the suction passes sonic it becomes a supersonic rooftop ended by a shock, which stands further aft the faster the flight and drops the pressure back to subsonic. In drier air only the pocket fogs, and its aft edge is the shock.
The cone
The fuselage, as a slender body of revolution. Its suction grows as its thickness squared times the log of one over β times its thickness, so it reaches sonic, its critical Mach number, only at about 0.96 for a fighter's fineness. Short of that the flow stays subsonic and recovers smoothly along the body, and it seldom fogs.
Past it a transonic pocket opens within a few hundredths of a Mach number. It keeps expanding until the shock that ends it, is felt further out the nearer Mach one, and is cut off by the shock: a cone opening aft, soft at its front and hard at its back. Past Mach one the pocket is the aft body's, ended by the tail's shock, and it is gone by about Mach 1.12. Accelerating through, it lasts a few seconds, as it does on film.
The captured wing
A capture reads the wing off the model in strips, and a fin's root or a fairing can make one strip thicker or longer than its neighbours. Each strip's thickness is capped at one and a half times the root's, and the table is smoothed along the span with a local straight-line fit over about a twentieth of it. A step in the table would otherwise stand in the vapor as a wall.
How high the sheet reaches is set by the chord, but never by more than the wing's mean chord: a field is felt about as far off as the patch making it is wide, and inboard, where the strake and the tail run together into one long chord the body carries, the local chord would stand the sheet up beside the fuselage. Its inboard edge also softens with height, about a metre wider per metre up, as the surface's pressure blurs the further off it is felt.
Keeping it finite
A linear theory's suction diverges at Mach one, so every deficit is eased into what an isentropic expansion to a local Mach 1.4 makes.
Behind a shock
A droplet doesn't vanish at a shock. It evaporates in the warmer air behind it, in about 3 ms for a micron's radius, which is a metre at 300 m/s. So behind the wing's shock and the cone's, the field relaxes over that length, growing with the droplets' radius squared, and the hard edge has the short tail photographs show.