Ababou, R., McLaughlin, D., Gelhar, L. W. & Tompson, A. F. B. 1989 Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media. Transp. Porous Media 4 (6), 549–565.
Andricevic, R. & Cvetkovic, V. 1998 Relative dispersion for solute flux in aquifers. J. Fluid Mech. 361, 145–174.
Attinger, S., Dentz, M., Kinzelbach, H. & Kinzelbach, W. 1999 Temporal behaviour of a solute cloud in a chemically heterogeneous porous medium. J. Fluid Mech. 386, 77–104.
Attinger, S., Dentz, M. & Kinzelbach, W. 2004 Exact transverse macro dispersion coefficients for transport in heterogeneous porous media. Stochastic Environ. Res. Risk Assessment 18 (1), 9–15.
Auriault, J. L. & Adler, P. M. 1995 Taylor dispersion in porous media: analysis by multiple scale expansions. Adv. Water Resour. 18 (4), 217–226.
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.
Beckie, R., Aldama, A. A. & Wood, E. F. 1996 Modeling the large-scale dynamics of saturated groundwater flow using spatial-filtering theory. 1. Theoretical development. Water Resour. Res. 32 (5), 1269–1280.
Bellin, A., Lawrence, A. E. & Rubin, Y. 2004 Models of sub-grid variability in numerical simulations of solute transport in heterogeneous porous formations: three-dimensional flow and effect of pore-scale dispersion. Stochastic Environ. Res. Risk Assessment 18 (1), 31–38.
Bellin, A., Salandin, P. & Rinaldo, A. 1992 Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations. Water Resour. Res. 28 (9), 2211–2227.
Bolster, D., Benson, D. A., Le Borgne, T. & Dentz, M. 2010 Anomalous mixing and reaction induced by superdiffusive nonlocal transport. Phys. Rev. E 82 (2), 21119.
Bolster, D., Dentz, M. & Le Borgne, T. 2009 Solute dispersion in channels with periodically varying apertures. Phys. Fluids 21, 056601.
Bolster, D., Valdés-Parada, F. J., LeBorgne, T., Dentz, M. & Carrera, J. 2011 Mixing in confined stratified aquifers. J. Contam. Hydrol. 120–121, 198–212.
Bras, R. L. & Rodríguez-Iturbe, I. 1994 Random Functions and Hydrology. Dover.
Chatwin, P. C. & Allen, C. M. 1985 Mathematical models of dispersion in rivers and estuaries. Annu. Rev. Fluid Mech. 17, 119–149.
Chatwin, P. C. & Sullivan, P. J. 1979 The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow. J. Fluid Mech. 91 (2), 337–355.
Cirpka, O. A. & Kitanidis, P. K. 2000 Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments. Water Resour. Res. 36 (5), 1221–1136.
Cushman, J. H. & Moroni, M. 2001 Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. I. Theory. Phys. Fluids 13, 75.
Cvetkovic, V. & Dagan, G. 1994 Transport of kinetically sorbing solute by steady random velocity in heterogenous porous formations. J. Fluid Mech. 265, 189–215.
Cvetkovic, V., Dagan, G. & Cheng, H. 1998 Contaminant transport in aquifers with spatially variable hydraulic and sorption properties. Proc. Math. Phys. Engng Sci. 454 (1976), 2173–2207.
Cvetkovic, V. & Shapiro, A. M. 1989 Solute advection in stratified formations. Water Resour. Res. 25 (6), 1283–1289.
Dagan, G. 1984 Solute transport in heterogeneous porous formations. J. Fluid Mech. 145, 151–177.
Dagan, G. 1987 Theory of solute transport by groundwater. Annu. Rev. Fluid Mech. 19, 183–215.
Dagan, G. 1989 Flow and Transport in Porous Formations. Springer.
Dagan, G. 1990 Transport in heterogeneous porous formations: spatial moments, ergodicity & effective dispersion. Water Resour. Res. 26 (6), 1281–1290.
Dagan, G. 1991 Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J. Fluid Mech. 233, 197–210.
Dagan, G. 1994 Transport by two-dimensional random velocity fields: effective dispersion coefficients of a finite plume. Stochastic Meth. Hydrol. Environ. Engng 2, 113–126.
Dagan, G. & Fiori, A. 1997 The influence of pore-scale dispersion on concentration statistical moments in transport through heterogeneous aquifers. Water Resour. Res. 33 (7), 1595–1605.
Dagan, G., Fiori, A. & Jankovic, I. 2003 Flow and transport in highly heterogeneous formations. Part 1. Conceptual framework and validity of first-order approximations. Water Resour. Res. 39 (9), 1268.
Dentz, M. & Carrera, J. 2007 Mixing and spreading in stratified flow. Phys. Fluids 19, 017107.
Dentz, M., Kinzelbach, H., Attinger, S. & Kinzelbach, W. 2000 a Temporal behaviour of a solute cloud in a heterogeneous porous medium. 1. Point-like injection. Water Resour. Res. 36 (12), 3591–3604.
Dentz, M., Kinzelbach, H., Attinger, S. & Kinzelbach, W. 2000 b Temporal behaviour of a solute cloud in a heterogeneous porous medium. 2. Spatially extended injection. Water Resour. Res. 36 (12), 3605–3614.
Dentz, M. & Tartakovsky, D. M. 2008 Self-consistent four-point closure for transport in steady random flows. Phys. Rev. E 77 (6), 66307.
de Dreuzy, J. R., Beaudoin, A. & Erhel, J. 2007 Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations. Water Resour. Res. 43, W10439.
Eberhard, J. 2004 Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media. J. Phys. A: Math. Gen. 37, 2549–2571.
Eberhard, J. 2005 Upscaling for stationary transport in heterogeneous porous media. Multiscale Model. Simulation (SIAM) 3 (4), 957–976.
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5 (4), 544–560.
Fiori, A. 1996 Finite Peclet extensions of Dagan's solutions to transport in anisotropic heterogeneous formations. Water Resour. Res. 32 (1), 193–198.
Fiori, A. 1998 On the influence of pore-scale dispersion in nonergodic transport in heterogeneous formations. Transp. Porous Media 30 (1), 57–73.
Fiori, A., Boso, F., de Barros, F. P. J., De Bartolo, S., Frampton, A., Severino, G., Suweis, S. & Dagan, G. 2010 An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity. Water Resour. Res. 46 (8), W08601.
Fiori, A. & Dagan, G. 2000 Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J. Contam. Hydrol. 45 (1–2), 139–163.
Fiori, A. & Dagan, G. 2002 Transport of a passive scalar in a stratified porous medium. Transp. Porous Media 47 (1), 81–98.
Fischer, H. B. 1973 Longitudinal dispersion and turbulent mixing in open-channel flow. Annu. Rev. Fluid Mech. 5 (1), 59–78.
Fischer, H. B., List, J. E., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Gelhar, L. W. & Axness, C. L. 1983 Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19 (1), 161–180.
Gotovac, H., Cvetkovic, V. & Andricevic, R. 2009 Flow and travel time statistics in highly heterogeneous porous media. Water Resour. Res. 45 (7), W07402.
Herrera, P. & Beckie, R. 2009 A new approach to model solute mixing in porous media. Eos Trans. AGU Fall Meet. Suppl., Abstract H23D-0990 90 (52).
Hou, Z. & Rubin, Y. 2005 On minimum relative entropy concepts and prior compatibility issues in vadose zone inverse and forward modeling. Water Resour. Res. 41 W12425.
Hsu, K. C., Zhang, D. & Neuman, S. P. 1996 Higher-order effects on flow and transport in randomly heterogeneous porous media. Water Resour. Res. 32 (3), 571–582.
Indelman, P. & Dagan, G. 1999 Solute transport in divergent radial flow through heterogeneous porous media. J. Fluid Mech. 384, 159–182.
Jaynes, E. T. 1957 Information theory and statistical mechanics. Phys. Rev. 108 (2), 171–190.
Kitanidis, P. K. 1988 Prediction by the method of moments of transport in a heterogeneous formation. J. Hydrol. 102 (1–4), 453–473.
Koch, D. L. & Brady, J. F. 1988 Anomalous diffusion in heterogeneous porous media. Phys. Fluids 31, 965.
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22.
Kramer, P. R., Majda, A. J. & Vanden-Eijnden, E. 2003 Closure approximations for passive scalar turbulence: a comparative study on an exactly solvable model with complex features. J. Stat. Phys. 111 (3), 565–679.
Kullback, S. 1997 Information Theory and Statistics. Dover.
Lawrence, A. E. & Rubin, Y. 2007 Block-effective macrodispersion for numerical simulations of sorbing solute transport in heterogeneous porous formations. Adv. Water Resour. 30 (5), 1272–1285.
Le Borgne, T., Dentz, M. & Carrera, J. 2008 Lagrangian statistical model for transport in highly heterogeneous velocity fields. Phys. Rev. Lett. 101 (9), 090601.
Majda, A. J. & Kramer, P. R. 1999 Simplified models for turbulent diffusion: theory, numerical modelling & physical phenomena. Phys. Rep. 314 (4–5), 237–574.
Matheron, G. & De Marsily, G. 1980 Is transport in porous media always diffusive: a counterexample. Water Resour. Res. 16 (5), 901–917.
McComb, W. D. 1990 The Physics of Fluid Turbulence. Clarendon Press.
Mole, N., Schopflocher, T. P. & Sullivan, P. J. 2008 High concentrations of a passive scalar in turbulent dispersion. J. Fluid Mech. 604, 447–474.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Munro, R. J., Chatwin, P. C. & Mole, N. 2003 A concentration PDF for the relative dispersion of a contaminant plume in the atmosphere. Boundary-Layer Meteorol. 106 (3), 411–436.
Neuman, S. P. 1990 Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour. Res. 26 (8), 1749–1758.
Neuman, S. P. 2006 Blueprint for perturbative solution of flow and transport in strongly heterogeneous composite media using fractal and variational multiscale decomposition. Water Resour. Res. 42 (6), W06D04.
Neuman, S. P. & Zhang, Y. K. 1990 A quasi-linear theory of non-Fickian and Fickian subsurface dispersion. 1. Theoretical analysis with application to isotropic media. Water Resour. Res. 26 (5), 887–902.
Phythian, R. & Curtis, W. D. 1978 The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow. J. Fluid Mech. 89 (02), 241–250.
Rajaram, H. & Gelhar, L. W. 1993 a Plume scale-dependent dispersion in heterogeneous aquifers 1. Lagrangian analysis in a stratified aquifer. Water Resour. Res. 29 (9), 3249–3260.
Rajaram, H. & Gelhar, L. W. 1993 b Plume scale-dependent dispersion in heterogeneous aquifers 2. Eulerian analysis and three-dimensional aquifers. Water Resour. Res. 29 (9), 3261–3276.
Risken, H. 1989 The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edn. Springer.
Rubin, Y. 1990 Stochastic modeling of macrodispersion in heterogeneous porous media. Water Resour. Res. 26 (1), 133–141.
Rubin, Y. 2003 Applied Stochastic Hydrogeology. Oxford University Press.
Rubin, Y., Bellin, A. & Lawrence, A. E. 2003 On the use of block-effective macrodispersion for numerical simulations of transport in heterogeneous formations. Water Resour. Res. 39 (9), 1242–1252.
Rubin, Y., Sun, A., Maxwell, R. & Bellin, A. 1999 The concept of block-effective macrodispersivity and a unified approach for grid-scale- and plume-scale-dependent transport. J. Fluid Mech. 395, 161–180.
Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33 (1), 289–317.
Valocchi, A. J. 1990 Numerical simulation of the transport of adsorbing solutes in heterogeneous aquifers. In Computational Methods in Subsurface Hydrology (ed. Gambolati, G. et al. ), chap. 9, pp. 373–382. Computational Mechanics.
Woodbury, A. D. & Ulrych, T. J. 1993 Minimum relative entropy: forward probabilistic modeling. Water Resour. Res. 29 (8), 2847–2860.
Zavala-Sanchez, V., Dentz, M. & Sanchez-Vila, X. 2009 Characterization of mixing and spreading in a bounded stratified medium. Adv. Water Resour. 32 (5), 635–648.