Multipoint concentration statistics for transport in stratified random velocity fields

Multipoint concentration statistics for transport in stratified random velocity fields.

We determine the full multipoint concentration statistics for superdiffusive transport in a steady stratified random velocity field. Using a Lagrangian approach, we derive explicit analytical expressions for the multipoint moments of concentration and specifically for the concentration variance, which is a measure for concentration uncertainty. The multipoint concentration moments are fully cha...

Concentration statistics for transport in random media.

We study the ensemble statistics of the particle density in a random medium whose mean transport dynamics describes a continuous time random walk. Starting from a Langevin equation for the particle motion in a single disorder realization, we derive evolution equations for the n-point moments of concentration by coarse graining and ensemble averaging the microscale transport problem. The governi...

Particle transport in a random velocity field with Lagrangian statistics.

The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried out in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turnover time. Various quantities such as the Batchelor constant and the dimensionless constants ent...

Heat and mass transport in nonhomogeneous random velocity fields.

The effective equation describing the transport of passive tracers in nonsolenoidal velocity fields is determined, assuming that the velocity field U(r,t) is a function of both position r and time t, albeit remaining locally random. Assuming a strong separation of scales and applying the method of homogenization, we find a Fickian constitutive relation for the coarse-grained particle flux, as t...

Markov Random Fields in Statistics