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 σ, is characterized at time τ by a folded normal radial density with parameter στ 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 τ>0 and distances L•• are derived and related to the Rayleigh and Maxwell laws associated with i.i.d. N(0,σ) velocity components.