Memory effects and ergodicity for diffusion in spatially correlated velocity fields

Abstract

We show that the process of diffusion in statistically homogeneous velocity fields with finite correlation range “remembers” the shape and the orientation of the source over hundreds of dimensionless times and behaves ergodically with respect to the one‐particle dispersion only asymptotically.

Authors

Nicolae Suciu
Friedrich-Alexander University of Erlangen-Nuremberg, Mathematics Department

Karl Sabelfeld
Weierstrass Institute for Applied Analysis and Stochastics
Institute of Computational Math. and Math. Geophysics, Siberian Branch Russian Acad.

Călin Vamoş
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Constantin Andronache
Boston College, 140 Commonwealth Avenue, Chestnut Hill, USA

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Cite this paper as:

N. Suciu, K. Sabelfeld, C. Vamoş, C. Andronache, Memory effects and ergodicity for diffusion in spatially correlated velocity fields, Proc. Appl. Math. Mech., 7 (2007), 2010015-2010016
doi: 10.1002/pamm.200700057

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Proc. Appl. Math. Mech.

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Wiley

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References

[1] J. Eberhard, N. Suciu, and C. Vamos, On the self-averaging of dispersion for transport in quasi-periodic random media, J. Phys. A: Math. Theor. 40, 597 (2007),
CrossRef (DOI).

[2] N. Suciu, C. Vamos¸, J. Vanderborght, H. Hardelauf, and H. Vereecken, Internal Report ICG-IV 00204, Forschungszentrum Julich (2004).

[3] N. Suciu, C. Vamos¸, J. Vanderborght, H. Hardelauf, and H. Vereecken, Numerical investigations on ergodicity of solute transport in heterogeneous aquifers, Water Resour. Res. 42, W04409 (2006),
CrossRef (DOI)

[4] N. Suciu and C. Vamos, Comment on “Nonstationary flow and nonergodic transport in random porous media” by G. Darvini and P. Salandin, Water Resour. Res., (2007),
CrossRef (DOI) (in press).

[5] C. Vamos¸, N. Suciu, and H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processes,  J. Comput. Phys. 186(2), 527 (2003).
CrossRef (DOI)

[6] C.L. Zirbel, Lagrangian observations of homogeneous random environments, Adv. Appl. Prob. 33, 810 (2001).
CrossRef (DOI)

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