TY - JOUR

T1 - The problem of moments and the Majda model for scalar intermittency

AU - Bronski, Jared C.

AU - McLaughlin, Richard M.

N1 - Funding Information:
Jared C. Bronski would like to acknowledge support from the National Science Foundation under grant DMS-9972869. Richard M. McLaughlin would like to acknowledge support from NSF Career Grant DMS-97019242, and would like to thank L. Kadanoff and the James Franck Institute for support during the writing of this paper. Both authors wish to thank M. Chertkov, L. Kadanoff, A. Majda, K. McLaughlin, R. Pierrehumbert, E. Tabak, and W. Young for helpful discussions.

PY - 2000/1/31

Y1 - 2000/1/31

N2 - An enormous and important theoretical effort has been directed at studying the origin of broad-tailed probability distribution functions observed for numerous physical quantities measured in fluid turbulence. Despite the amount of attention this problem has received, there are still few rigorous results. One model which has been amenable to rigorous analysis is the Majda model for the diffusion of a passive scalar in the presence of a random, rapidly fluctuating linear shear layer, an anisotropic analog of the Kraichnan model. Previous work, by Majda, lead to explicit formulas for the moments of the distribution of the scalar. We examine this model, and construct the explicit large moment number asymptotics. Using properties of entire functions of finite order, we calculate the rigorous tail of the limiting probability distribution function for normalized scalar fluctuations. Through this process, we obtain an explicit relation between the limiting tail of the scalar probability distribution function and that of the scalar gradient. We additionally apply the method to moments derived asymptotically by Son, and those derived phenomenologically by She and Orszag. (C) 2000 Elsevier Science B.V.

AB - An enormous and important theoretical effort has been directed at studying the origin of broad-tailed probability distribution functions observed for numerous physical quantities measured in fluid turbulence. Despite the amount of attention this problem has received, there are still few rigorous results. One model which has been amenable to rigorous analysis is the Majda model for the diffusion of a passive scalar in the presence of a random, rapidly fluctuating linear shear layer, an anisotropic analog of the Kraichnan model. Previous work, by Majda, lead to explicit formulas for the moments of the distribution of the scalar. We examine this model, and construct the explicit large moment number asymptotics. Using properties of entire functions of finite order, we calculate the rigorous tail of the limiting probability distribution function for normalized scalar fluctuations. Through this process, we obtain an explicit relation between the limiting tail of the scalar probability distribution function and that of the scalar gradient. We additionally apply the method to moments derived asymptotically by Son, and those derived phenomenologically by She and Orszag. (C) 2000 Elsevier Science B.V.

KW - Long tails

KW - Passive scalar intermittency

KW - Turbulence

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U2 - 10.1016/S0375-9601(99)00907-X

DO - 10.1016/S0375-9601(99)00907-X

M3 - Article

AN - SCOPUS:0034736942

VL - 265

SP - 257

EP - 263

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 - 4

ER -