ON MARKOV MODELING OF TURBULENCE

We consider Lagrangian stochastic modelling of the relative motion of two fluid particles in the inertial range of a turbulent flow. Euleria n analysis of such modelling corresponds to an equation for the Euleri an probability distribution of velocity-vector increments which introd uces a hierarchy of constraints for making the model consistent with r esults from the theory of locally isotropic turbulence. A nonlinear Ma rkov process is presented, which is able to satisfy exactly, in the st atistical sense, incompressibility, the exact results on the third-ord er structure function, and the experimental second-order statistics. T he corresponding equation for the Eulerian probability density of velo city-vector increments is solved numerically. Numerical results show n on-Gaussian statistics of the one-dimensional Lagrangian probability d istributions, and a complex shape of the three-dimensional Eulerian pr obability density function. The latter is then compared with existing experimental data.