You're probably best off using particles to hold the color, then using the aero velocities (I'd run this as a particle simulation after the aero sim) to advect the particles.
So first thing would be to start with a particle source that's the same as your aero source (say like a mesh with color) and have the particles use the emit location to sample your colorset. Then once that works, feed those points to the particle solver, and use a volume_influence field with a drag to force the particles to follow the volume sim (see attached, it doesn't need to be vdb, bob will work as well).
Then rasterize the color property on the particles to a volume with point_to_volume.
One thing I found was that I had to turn up the drag influence fairly high (like 100 or something - not totally sure why but that made it work well enough for my needs). The other gotcha is you may need to scale velocity by your simulation speed (say if your aero timescale was slower or faster). There are probably lots of places to fall of the wagon here depending on what is going on in your aero sim, but you'll need to experiment a bit. I'm not 100% sure the particles track the velocity field in a 1:1 way, but I'm also not sure that it always needs to be 100 % either the further you go from the source.
-T
