Speed and shear

Speed, and the two ways a flow field shearsCopy Anchor Link

The exhaust ran at 11 m/s, a sixtieth of what leaves a real afterburner, and it looked exactly like what it was: slow motion. It could not go faster because a noise field advected past about a fifth of its own period per frame strobes rather than flows.

The way out is the shutter. A feature that travels while the shutter is open is not recorded where it was — it is recorded that much longer. Stretching the domain by exactly that is what a camera does to anything moving, so the period along the flow grows with the speed and the ratio that has to stay under a fifth stays put however fast the gas goes. It is also the whole visual language of speed: fast gas is streaked gas. It costs nothing — no second lookup, just a longer period.

That bought 11 m/s → 300, measured as nineteen times the per-frame motion with the camera held still, and no strobing (gap1 well under gap5).

The ratio that has to stay under a fifth settles at 1 / (60 * eddyStretch * shutterS) however fast the flow goes — 0.13 at the defaults. The speed is not what limits this. What does are two things that have no shutter of their own:

• The wander. wander_noise is one-dimensional and unblurred, so its wavelength has to grow with the speed by hand: sway_scale_m is 19 m at 300 m/s, which keeps it moving a sixth of a wander per frame.
• How much axial structure is left. At 300 m/s the axial period is 37 m against a 13 m plume, so there is under half of one along it. The lateral filaments carry the texture from here on, which is exactly why they are what the field is built from.

The trap is that a flow field can shear in two different ways, and this one did both before it worked. Anything that varies along the plume must not divide or multiply the time term.

• The velocity gradient. A jet decelerates, so the obvious move is to subtract time * speed(x). That is not a flow: each station advects at its own rate, so the field is sheared a little further every second until the tail is a comb of stripes finer than anything that was ever in it. What convects rigidly is the travel time to a station, which for a linear velocity profile is a logarithm — plume_station. The time term is then the same everywhere.
• The period. Same mistake one level down, and much less obvious. The axial coordinate was divided by a period built from the local eddy scale and the local speed. The time term is enormous — 85 m/s is nearly a kilometre by ten seconds in — so dividing it by something that varies along the plume varies the quotient in proportion, and the comb comes straight back. plume_flow_period is deliberately built from the nozzle's numbers alone and used everywhere.

The eddies still coarsen downstream. That is the lateral scale's job, and the lateral coordinate carries no time term, so nothing shears.

Why the texture is filaments, and why that is what lets it go fastCopy Anchor Link

The shutter buys speed by lengthening features along the flow, so at 165 m/s the axial period is over twenty metres — longer than the plume. Anything relying on axial detail is gone.

Which is fine, because a real exhaust's texture is not axial. It is longitudinal filaments: fine across the flow, drawn out to nothing along it. Look at any launch photograph. And a filament that runs along the flow is invariant to being blurred along the flow — so the lateral detail survives whatever the speed is.

That is the whole reason the plume can be this fast and still look like something. The dials that do it are turbulence_scale_m at 0.16 (fine across) against eddyStretch at 9 (long along), which is a sixty to one aspect ratio before the shutter has its say.

It also means the tail should close, not billow. plume_spread came back down to 0.18: a column of filaments drawing to a point is what the reference looks like, and a wide turbulent bell is what a much slower jet looks like. The side effect is a much smaller hull, which paid for the third octave of noise twice over — 3.7MP went from 28.1 to 33.9 fps.

Both failures look identical — a regular comb of stripes in the tail, spacing growing downstream — and neither looks like a flow bug. The tell is that they get finer the longer the scene runs.