insu-03572264
https://insu.hal.science/insu-03572264
https://insu.hal.science/insu-03572264/document
https://insu.hal.science/insu-03572264/file/PhysRevFluids.7.024501.pdf
doi:10.1103/PhysRevFluids.7.024501
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Impact of velocity correlations on longitudinal dispersion in space-Lagrangian advective transport models
Aquino, Tomás
Velásquez-Parra, Andrés
[PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
[SDU.STU.HY] Sciences of the Universe [physics]/Earth Sciences/Hydrology
ART
Space-Lagrangian random walk models conceptualize advective transport in terms of collections of particles undergoing fixed-length steps along flow streamlines. The statistics and correlation structure of the underlying flow velocity statistics determine the transit times of particles undergoing advective transport. Broad velocity distributions lead to broadly-distributed step transit times, reproducing commonly observed anomalous transport features such as superdiffusive plume growth, which are not captured by classical Fickian theories. Early space-Lagrangian models considered uncorrelated velocities across steps. These approaches were later extended to account for correlations through a spatial-Markov process. Here, we compare longitudinal dispersion dynamics in an uncorrelated continuous time random walk with fixed space steps to a Bernoulli relaxation spatial-Markov model exhibiting exponential decay of spatial velocity correlations along streamlines. We provide rigorous theoretical derivations, validated against numerical simulations. We find that, although the scaling forms of asymptotic dispersion agree between the two models, exact asymptotic equivalence requires employing different correlation lengths, which depend on the underlying Eulerian velocity statistics. The two models become equivalent in the limit of very broad velocity distributions, corresponding to a new quasi-ballistic regime recently identified in unsaturated porous media.
2022
2022-02-14
en
Physical Review Fluids
American Physical Society