Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem.

We consider the transport of dynamically passive quantities in the Batchelor regime of a smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity, we formulate the statistics of relevant characteristics of Lagrangian motion. This allows us to generalize many results obtained previously for strain delta correlated in time, thus answering a question about the universality of these results.

[1]  A. Fouxon.  Evolution of a scalar gradient’s probability density function in a random flow , 1998 .

[2]  Physics Letters , 1962, Nature.

[3]  M. Chertkov,et al.  INTERMITTENT DISSIPATION OF A PASSIVE SCALAR IN TURBULENCE , 1998 .

[4]  Lebedev,et al.  Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Passive scalar in a large-scale velocity field , 1998, chao-dyn/9810019.

[6]  Robert H. Kraichnan,et al.  Small‐Scale Structure of a Scalar Field Convected by Turbulence , 1968 .

[7]  Steven A. Orszag,et al.  Stability and Lyapunov stability of dynamical systems: A differential approach and a numerical method , 1987 .

[8]  Yakhot,et al.  Limiting probability distributions of a passive scalar in a random velocity field. , 1989, Physical review letters.

[9]  G. Batchelor.  Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity , 1959, Journal of Fluid Mechanics.

[10]  V. Lebedev,et al.  Large-scale properties of passive scalar advection , 1999, chao-dyn/9901027.

[11]  M. Chertkov,et al.  Exact field-theoretical description of passive scalar convection in an N-dimensional long-range velocity field , 1994 .

[12]  Robert H. Kraichnan,et al.  Convection of a passive scalar by a quasi-uniform random straining field , 1974, Journal of Fluid Mechanics.

[13]  Denis Bernard,et al.  Slow Modes in Passive Advection , 1998 .

[14]  Shraiman,et al.  Lagrangian path integrals and fluctuations in random flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[16]  Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow , 1997, chao-dyn/9706017.

[17]  Turbulent decay of a passive scalar in the Batchelor limit: Exact results from a quantum-mechanical approach , 1998, physics/9806047.