Diffusion by Continuous Movements

The influence of velocity distribution on one‐particle dispersion is studied. The ensemble of particle releases is subdivided into subensembles characterized by particle velocity at the instant of release. Under certain simplifying assumptions, the motion of the particles of each subensemble is a systematic drift, combined with dispersal about the subensemble drift position. The displacement variance due to subensemble drift is dominant for small time t since particle release, whereas that due to subensemble is the more important at large t. The assumption that subensemble dispersal is Gaussian yields an estimate of the probability distribution density function θ(x, t) governing particle position which is correct both in the limits of t small and t large. The estimate is thus better than that given by the usual assumption that θ is Gaussian, and appears useful for t values less than the Lagrangian integral scale. The subensemble approach offers some new insights into the problem of the instantaneous struc...