TY - JOUR

T1 - Exact field-theoretical description of passive scalar convection in an N-dimensional long-range velocity field

AU - Chertkov, Michael

AU - Gamba, Andrea

AU - Kolokolov, Igor

PY - 1994/9/12

Y1 - 1994/9/12

N2 - We describe a new functional integral method for the computation of averages containing chronological exponentials of random matrices of arbitrary dimension. We apply these results to the rigorous study of the statistics of a passive scalar advected by a large-scale N-dimensional flow. In the delta-correlated case the statistics of the rate of line stretching appears to be exactly Gaussian at all times and we explicitly compute the dependence of the mean value and variance of the stretching rate on the space dimension N. The probability distribution function of the passive scalar is also exactly computed. Further applications of our functional integral method are suggested.

AB - We describe a new functional integral method for the computation of averages containing chronological exponentials of random matrices of arbitrary dimension. We apply these results to the rigorous study of the statistics of a passive scalar advected by a large-scale N-dimensional flow. In the delta-correlated case the statistics of the rate of line stretching appears to be exactly Gaussian at all times and we explicitly compute the dependence of the mean value and variance of the stretching rate on the space dimension N. The probability distribution function of the passive scalar is also exactly computed. Further applications of our functional integral method are suggested.

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U2 - 10.1016/0375-9601(94)90233-X

DO - 10.1016/0375-9601(94)90233-X

M3 - Article

AN - SCOPUS:0001042577

VL - 192

SP - 435

EP - 443

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 5-6

ER -