Disturbance

DisturbanceCopy Anchor Link

A shape with noise on it is not a jet. Five things separate the two, and each one is a piece of flow physics rather than a look.

The potential coreCopy Anchor Link

A jet leaves the nozzle as laminar flow with a mixing layer only at its edge, and that layer eats inward until it reaches the axis about five diameters down. Before it does, the core is smooth; after it, the whole cross-section is turbulent. So the interior disturbance is weighted:

float mixed = smoothstep(0.0, uCorePotential, along);
float edge = smoothstep(uCoreEdge, 1.0, radial / radius);

float shear = mix(edge, 1.0, mixed);

Stirring the core from the lip is what made the first version one uniform cloud of noise end to end, with no difference between the part that is still a jet and the part that is already weather. This is also what lets the root read as hot and solid while the tail reads as torn.

The core is also a cone, and the temperature profile has to say so. It used to be a top hat over the whole half-width, relaxing to a Gaussian by the end of the core. Because the half-width grows downstream, the hot region widened with it, and a fighter's plume read as a long, even barrel. Now the core's radius closes linearly from the nozzle's at the lip to nothing at the end of the core. Across the mixing layer, from the core's edge to the half-width, the gas falls as a Gaussian. Past the core that is the far field's own Gaussian, so nothing downstream changes. The hot, bright part is then the narrowing cone that every photograph of a reheat flame shows, and that flight sims draw.

The mixing layer is also hotter than a straight blend of jet and air. The friction that slows the jet turns its speed back into heat. With a Prandtl number near one, the total enthalpy mixes the way the velocity does (Crocco and Busemann). Gas that is a share f exhaust keeps f of the jet's kinetic energy but moves at only f of its speed, so f(1 − f) of that energy is now heat:

T = T_air + f · (T_jet − T_air) + 4 f (1 − f) · (afterburningK + Δu² / 8 c_p)

Δu is the jet's speed over the air, and c_p its heat capacity. The friction term has the same shape as the fuel still burning, peaking at an even mix. It is worth about 160 K on a fighter at full reheat on the ground, 100 K at Mach one, and 500 K round a kerosene rocket. Planck's law is steep enough that this makes the sheath several times brighter than the blend alone.

Eddies are stretched, and they coarsenCopy Anchor Link

A jet stretches what is in it, so the noise domain is stretched the same way — uEddyStretch divides only the axial coordinate. Isotropic noise reads as smoke sitting behind an aircraft; the same field at three to one reads as gas being dragged out of a pipe. And the mixing layer thickens downstream, so uEddyGrowth coarsens the scale with along: one eddy at the lip is not one eddy at the tail.

The helical modeCopy Anchor Link

A round jet's first instability is helical, not random. The column winds about its own axis and the wind runs aft with the flow, so plume_drift carries a deterministic corkscrew underneath its broadband noise:

float turn = TAU * (uHelixTurns * station / v_plume.x - uTime * ...);

drift += vec2(cos(turn + seed), sin(turn + seed)) * v_disturb.z;

Noise alone gives a plume that wobbles. This is what makes one turn.

The train starts aft of the lipCopy Anchor Link

A shock train stands about a nozzle diameter downstream of the exit plane, never on it. shock_onset is that delay, and without it the plume is a string of beads that begins inside the can — which is the single thing that made the first thin version read as a machined part rather than as gas.

shock_growth is the other half: real trains stretch hard as the jet slows, and evenly spaced cells all the way down read as a ruler however well shaded.

The cells breatheCopy Anchor Link

The nozzle pressure ratio is never quite steady, so the whole shock train slides fore and aft a fraction of a spacing. cell_jitter is that. Without it the disks are a ruler laid down the plume, and a ruler is the one thing in the picture that could not be gas.

The tail lets go — and it has to have something to let go withCopy Anchor Link

This is the piece that took two attempts. A jet does not end in a point. The supersonic core closes, and what is left spreads as it entrains the air around it: a real plume is at its widest where it has stopped being a jet.

plume_body_radius is therefore a closing core plus an opening mixing region:

float close = pow(max(0.0, 1.0 - along), uTaperPower);
float spread = uPlumeSpread * along * along;

return v_plume.y * (grow * close + spread);

Three things had to follow from it, and none of them work without the others:

• The chew climbs instead of fading. It used to fade past churn_peak, because chewing a tail that had closed to a fraction of a nozzle punched straight through it into rings. The tail has body again, so the reason is gone and the opposite is what is wanted — tail_churn makes the mixing region a couple of times more agitated than the barrel, which is the real difference between a supersonic column and what follows it.
• The emission cannot end with the fire. The burn decay times 1 - t² goes to zero at the tip whatever else happens, so the spread was opening out into something completely invisible and the plume still read as a streak that simply stopped. tail_glow is a second, dimmer term gated to the same region: what is no longer burning but is still hot, which is the part that churns.
• The diamonds have to be out of the way. shock_decay at 4.2 keeps the train inside the first third. Left running the whole length it competes with the break-up and the plume reads as a rope with beads on it.

The hull follows: with a spread the frustum can no longer close to a point, so hull_taper returns spread / (1 + spread). Costs about 30% more fragment work — 3.7MP went from 36.5 to 28.1 fps — which the frame had.

The rate a corkscrew can actually be drawn atCopy Anchor Link

helix_hz, and emphatically not the sway's own speed over its own scale. That works out at about seven revolutions a second, which is forty degrees of phase between one frame and the next. The real instability genuinely is that fast; at sixty frames a second it aliases, and what it looks like is the column snapping about laterally at random rather than winding — worst right where the plume is widest and the eye is already looking. Under a hertz is what can be drawn. The wander had the same problem for the same reason and its speed came down with it.