TY - JOUR

T1 - Inertial-Range Behavior of a Passive Scalar Field in a Random Shear Flow: Renormalization Group Analysis of a Simple Model

AU - Antonov, N. V.

AU - Malyshev, A. V.

PY - 2012

Y1 - 2012

N2 - Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form (t−t)kd−1+, where k ⊥=|k ⊥| and k ⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity.

AB - Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form (t−t)kd−1+, where k ⊥=|k ⊥| and k ⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity.

KW - Renormalization group – Turbulent transport – Anomalous scaling

U2 - 10.1007/s10955-011-0399-0

DO - 10.1007/s10955-011-0399-0

M3 - Article

VL - 146

SP - 33

EP - 55

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -