I came across this just now when looking for info on noise fields. I've never heard of this before; looks very interesting.
Noise fields are really rewarding to add to a particle system since you get the effect of fluid/air dynamic for a fraction of the cost and you can move though the flow field as you see fit. Both forward and backwards in time.
Xetick, do you need to recalculate the noise field each frame?
Not really. But if you do you can simulate wind/turbulence. If that is noticeable at all depends on the amount of particles. If you inject a lot in a static noise field you will clearly see pathsforms.
Worth noting is that in the post they use a single noise value and transform that into an angle. I found such a system complicated to control in a good way, at least in 3d. Part of the problem is that you put limits of how the particle is allowed to change its velocity. For example to be able to rotate from 359 deg to 0 deg you would have to rotate 'all the way back' or have a 'speed' of over 1.0.
My system gets 3 independent 3d noisefield values. It's a bit more to compute but you can easily control each axis by itself.