Persistence of incomplete mixing: a key to anomalous transport.

Anomalous dispersion in heterogeneous environments describes the anomalous growth of the macroscopic characteristic sizes of scalar fields. Here we show that this phenomenon is closely related to the persistence of local scale incomplete mixing. We introduce the mixing scale ε as the length for which the scalar distribution is locally uniform. We quantify its temporal evolution due to the competition of shear action and diffusion and compare it to the evolution of the global dispersion scale σ. In highly heterogeneous flow fields, for which the temporal evolution of σ is superdiffusive, we find that ε evolves subdiffusively. The anomalous evolutions of the dispersion and mixing scales are complementary, εσ ∝ t. This result relates anomalous global dispersion to the dynamics of local mixing.

[1]  M. Dentz,et al.  Distribution- versus correlation-induced anomalous transport in quenched random velocity fields. , 2010, Physical review letters.

[2]  G. Iafrate,et al.  Bloch electron spontaneous emission from a single energy band in a classical ac field , 2009 .

[3]  Tanguy Le Borgne,et al.  Spatial Markov processes for modeling Lagrangian particle dynamics in heterogeneous porous media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Tanguy Le Borgne,et al.  Lagrangian statistical model for transport in highly heterogeneous velocity fields. , 2008, Physical review letters.

[5]  Daniel M Tartakovsky,et al.  Stochastic langevin model for flow and transport in porous media. , 2008, Physical review letters.

[6]  Is turbulent mixing a self-convolution process? , 2008, Physical review letters.

[7]  C. Reichhardt,et al.  Enhancing mixing and diffusion with plastic flow. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  A. Pikovsky,et al.  Mixing-induced global modes in open active flow. , 2007, Physical review letters.

[9]  Coarse grained scale of turbulent mixtures. , 2006, Physical review letters.

[10]  X. Sanchez‐Vila,et al.  Representative hydraulic conductivities in saturated groundwater flow , 2006 .

[11]  Haitao Xu,et al.  The Role of Pair Dispersion in Turbulent Flow , 2006, Science.

[12]  R. Lima,et al.  Chaotic advection and targeted mixing. , 2005, Physical review letters.

[13]  Application of the finite-size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  A J McKane,et al.  Stochastic models in population biology and their deterministic analogs. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  S. Pope.  Turbulent Flows: FUNDAMENTALS , 2000 .

[16]  Cristóbal López,et al.  Smooth-filamental transition of active tracer fields stirred by chaotic advection , 1999, chao-dyn/9906019.

[17]  Peter K. Kitanidis,et al.  The concept of the Dilution Index , 1994 .

[18]  J. Bouchaud,et al.  Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .

[19]  J. Ottino.  Mixing, chaotic advection, and turbulence , 1990 .

[20]  M. Toda,et al.  In: Statistical physics II , 1985 .

[21]  Sidney Redner,et al.  Scaling approach for the kinetics of recombination processes , 1984 .

[22]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[23]  M. Nelkin,et al.  Decay of scalar variance in terms of a modified Richardson law for pair dispersion , 1981 .