Journal of Fluid Mechanics

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

M. S.  Borgas a1 and B. L.  Sawford a1
a1 CSIRO Division of Atmospheric Research, FBI Mordialloc, Victoria 3195, Australia

Article author query
borgas ms   [Google Scholar] 
sawford bl   [Google Scholar] 


A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

(Published Online April 26 2006)
(Received April 30 1993)
(Revised May 30 1994)