Probabilistic profiles of continuously replenished spherically symmetric clouds

The evolution of a spherically symmetric cloud, continuously replenished from a Gaussian source with particle speed parameter ., is characterized at time . by a folded normal radial density with parameter .. and constant growth rates for p-percentile envelopes. Density functions for the speed of particles seen in profile by an optical sensor with a 4. steradian field of view at various times .>0 and distances L . . are derived and related to the Rayleigh and Maxwell laws associated with i.i.d. N(0, .) velocity components.