Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection

Abstract

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of $\xi$, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.

arXiv commentLatex (11pt) 43 pages, 22 figures (Feynman diagrams). The reader interested in the technical details of the calculations presented in the paper may want to visit: http://www.math.helsinki.fi/mathphys/paolo_files/passive_scalar/passcal.html

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• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
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• From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
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