Dispersion is a measure of how a plume spreads due to the  combination of spatial variations in the velocity field and diffusion. Anomalous (or non-Fickian) dispersion refers to cases where the plume spreading scales in a manner that differs from what one would expect from Fickian dispersion theory.

Below are two videos from a study where  we study the influence of curvature on the boundary on dispersion. The left video is for parabolic flow in a smooth two dimensional  channel. The right hand video shows the case where boundary  fluctuations are sufficiently large to generate recirculation zones. Interestingly, we find that boundary fluctuations do not always increase  dispersion (wider plume) as is the case here. Smaller fluctuations can  actually lead to decreases in dispersion. This has important implications as it suggests that more curvature in  the flow field (typical the more heterogeneous a medium) does not  automatically mean larger dispersion. It can also be seen as a  conceptual model of what occurs at the microscale in a porous medium.

Relevant Papers

D Bolster, MM Meerschaert & A Sikorskii
Product Rule for Vector Fractional Derivatives, Fractional Calculus & Applied Analysis, In Press

D Bolster and M Dentz
Anomalous Dispersion in Chemically Heterogeneous Media induced by Long Range Correlations, Journal of Fluid Mechanics, Volume 695, pp 366 - 389

D. Bolster, P. de Anna, D.A. Benson and A.M. Tartakovsky
Incomplete Mixing and Reactions with Fractional Dispersion, Advances in Water Resources, 37 (2012) 86–93

T. Le Borgne, D. Bolster, M. Dentz, P. de Anna and A. Tartakovsky,
Effective Pore-Scale Dispersion Upscaling with a Correlated CTRW Approach
Water Resources Research, 47, W12538, doi:10.1029/2011WR010457

D Bolster, M Dentz and T Le Borgne
Hyper Mixing in Shear Flow Sites
Water Resources Research, Water Resour. Res., 47, W09602, doi:10.1029/2011WR010737

T Le Borgne, M Dentz, P, D Bolster, J Carrera, JR de Dreuzy and O Bour
Persistence of incomplete mixing: A key to anomalous transport
Physical Review E, 84, 015301(R)

D Bolster, I Neuweiler, M Dentz, J Carrera
The Impact of Buoyancy on Front Spreading in Heterogeneous Porous Media in Two-Phase Immiscible Flow
Water Resources Research, 47, W02508, doi:10.1029/2010WR009399, 2011

D. Bolster, F.J. Valdes-Parada, T. Le Borgne, M. Dentz and J.Carrera
Mixing in Confined Stratified Aquifers
Journal of Contaminant Hydrology, doi: 10.1016/j.jconhyd.2010.02.003, Volumes 120-121, Pages 198-212

M Dentz, D Bolster
Distribution- versus correlation-induced anomalous transport in quenched random velocity fields
Physical Review Letters, 105, 244301

T Le Borgne, M Dentz, D Bolster, J Carrera, J-R de Dreuzy and P Davy
Non-Fickian mixing: temporal evolution of the scalar dissipation rate in porous media
Advances in Water Resources, doi:10.1016/j.advwatres.2010.08.006, Vol 33(12), P1468-1475

D Bolster, DA Benson, T LeBorgne and M Dentz
Anomalous mixing and reaction induced by superdiffusive nonlocal transport
Physical Review E, 82, 021119

Donado LD, Sanchez-Vila X, Dentz M, Carrera J and Bolster D
'Multi-component reactive transport in multi-continuum media'
Water Resources Research, 45, W11402, doi:10.1029/2008WR006823

Bolster D, LeBorgne T and Dentz M (2009)
'Solute dispersion in channels with periodically varying apertures'
Physics of Fluids, 21, 056601

Bolster D., Dentz M., Carrera J (2009)
"Effective Two-Phase flow in heterogeneous media under temporal pressure fluctuations"
Water Resources Research, 45, W05408, doi:10.1029/2008WR007460.