A FAMILY OF STOCHASTIC-MODELS FOR 2-PARTICLE DISPERSION IN ISOTROPIC HOMOGENEOUS STATIONARY TURBULENCE

A family of Lagrangian stochastic models for the joint motion of parti cle 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 th e particle accelerations. Two constraints are derived which formally r equire that the correct one-particle statistics are obtained by the mo dels. These constraints involve the Eulerian expectation of the 'accel eration' of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. Th e Navier-Stokes equations, with Gaussian Eulerian probability distribu tions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calc ulations show that the constraints do not always guarantee good one-pa rticle statistics, but it is possible to select a constrained model th at does. Thomson's model has good one-particle statistics, but is show n to have unphysical conditional accelerations. Comparisons of relativ e dispersion for the models are made.