Some relations between Lagrangian models and synthetic random velocity fields

The authors propose an alternative interpretation of Markovian transport models based on the well-mixed condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space-time increments. This interpretation allows direct association of the drift and noise terms entering the model, with the geometry of the turbulent fluctuations. In particular, the well-known nonuniqueness problem in the well-mixed approach is solved in terms of the antisymmetric part of the velocity correlations; its relation with the presence of nonzero mean helicity and other geometrical properties of the flow is elucidated. The well-mixed condition appears to be a special case of the relation between conditional velocity increments of the random field and the one-point Eulerian velocity distribution, allowing generalization of the approach to the transport of nontracer quantities. Application to solid particle transport leads to a model satisfying, in the homogeneous isotropic turbulence case, all the conditions on the behavior of the correlation times for the fluid velocity sampled by the particles. In particular, correlation times in the gravity and in the inertia dominated case, respectively, longer and shorter than in the passive tracer case; in the gravity dominated case, correlation times longer for velocity components along gravity, than for the perpendicular ones. The model produces, in channel flow geometry, particle deposition rates in agreement with experiments.