Fiddled with the shader and stuff a bit, right now it's really a kludge but it doesn't look like a dust storm anymore.
The smoke.influences.turbulence doesn't seem to have an effect on the dispersion of the smoke, unless I'm misinterpreting it. (I would consider turbulence a random change in velocity in this application)
What the smoke needs is a smooth fade to nothingness, or what I'd call "conservation of smoke":
As the particle gets larger, it should also get more transparent. Since each particle spawned is some physical amount of smoke, it should probably drop off proportional to the area covered by the particle. Or, growth^-2. Then it can naturally disappear.
If the initial "quantity" of smoke is determined by the sliding (more slip/hotter tire = more smoke per particle, ie spawning with higher alpha) then for the regular growth rate it can fade naturally into invisibility without needing an explicit life span.
Also have a question about the LightingSun function:
It takes lightColor as an input and outputs diffuse.
Why is the baseCol then multiplied by both? (baseCol*diffuse*lightColor)
Am I misinterpreting what diffuse means, or should it already be taking into account the color of the light source, and not need to be multiplied again.