TY - JOUR

T1 - Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar

AU - Chertkov, M.

AU - Falkovich, G.

AU - Kolokolov, I.

AU - Lebedev, V.

PY - 1995

Y1 - 1995

N2 - For a -function-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus find the dependence of the four-point correlation function on the diffusion and pumping scale for large space dimensionality d. It is shown that anomalous scaling appears in the first order of 1/d perturbation theory. Anomalous dimensions are found analytically both for the scalar field and for its derivatives, in particular, for the dissipation field.

AB - For a -function-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus find the dependence of the four-point correlation function on the diffusion and pumping scale for large space dimensionality d. It is shown that anomalous scaling appears in the first order of 1/d perturbation theory. Anomalous dimensions are found analytically both for the scalar field and for its derivatives, in particular, for the dissipation field.

UR - http://www.scopus.com/inward/record.url?scp=33744520912&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.52.4924

DO - 10.1103/PhysRevE.52.4924

M3 - Article

AN - SCOPUS:33744520912

VL - 52

SP - 4924

EP - 4941

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

ER -