Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field

Abstract

A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation function is described by an infinite family of scaling exponents, which satisfy exact transcendental equations derived explicitly in d dimensions. The exponents are organized in a hierarchical order according to their degree of anisotropy, with the spectrum unbounded from above and the leading exponent coming from the isotropic sector. For the higher-order structure functions, the anomalous scaling behavior is a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators, whose negative critical dimensions determine the exponents. A close formal resemblance of the model with the stirred NS equation reveals itself in the mixing of operators. Using the RG, the anomalous exponents are calculated in the one-loop approximation for the even structure functions up to the twelfth order.

37 pages, 4 figures, REVTeX

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Cited by in corpus (14)

• Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
• Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ${\epsilon }^3$
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• Pressure and intermittency in passive vector turbulence
• Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
• Influence of helicity on anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
• Anomalous scaling and anisotropy in models of passively advected vector fields
• Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy
• Anomalous scaling in statistical models of passively advected vector fields
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
• Steady state existence of passive vector fields under the Kraichnan model
• Renormalization group in the infinite-dimensional turbulence: third-order results