We develop a continuous time random walk (CTRW) approach for the evolution of
Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation …

An exact relation is derived between scalar dissipation due to molecular diffusivity and the
randomness of stochastic Lagrangian trajectories for flows without bounding walls. This …

Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in
1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows …

We provide analytical results for the ensemble-averaged and time-averaged squared
displacement, and the randomness of the latter, in the full two-dimensional parameter space …

The Richardson-scaling law states that the mean square separation of a fluid particle pair
grows according to t3 within the inertial range and at intermediate times. The theories …

Countless processes in nature and industry, from rain droplet nucleation to plankton
interaction in the ocean, are intimately related to turbulent fluctuations of local …

We study the origins of anomalous dispersion in heterogeneous porous media in terms of
the medium and flow properties. To identify and quantify the heterogeneity controls, we …

Canopy flows in the atmospheric surface layer play important economic and ecological
roles, governing the dispersion of passive scalars in the environment. The interaction of high …

We study the relation between flow structure and fluid deformation in steady flows through
two-dimensional heterogeneous media, which are characterized by a broad spectrum of …

We investigate the nonergodicity of the generalized Lévy walk introduced by Shlesinger et
al.[Phys. Rev. Lett. 58, 1100 (1987) PRLTAO 0031-9007 10.1103/PhysRevLett. 58.1100] …