Instanton for random advection

Abstract

A path integral over trajectories of $2n$ fluid particles is identified with a $2n$-th order correlation function of a passive scalar convected by $d$-dimensional short-correlated multi-scale incompressible random velocity flow. Strong intermittency of the scalar is described by means of an instanton calculus (saddle point $+$ fluctuations about it) in the path integral at $n\gg d$. Anomalous scaling exponent of the $2n$-th scalar's structural function is found analytically.

17 pages, RevTex 3.0, Submitted to Phys.Rev.E

References in corpus (6)

• Instantons in Burgers Equation
• Instantons and Intermittency
• Anomalous Scaling Exponents of a White-Advected Passive Scalar
• Anomalous Scaling in the N-Point Functions of Passive Scalar
• Symmetry and Scaling of Turbulent Mixing
• Non-universality of the scaling exponents of a passive scalar convected by a random flow

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• Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
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• Inverse cascade and intermittency of passive scalar in 1d smooth flow
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• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• Stirring up trouble: Multi-scale mixing measures for steady scalar sources
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• Instanton Calculus in Shell Models of Turbulence
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• A Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields
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• Mixing effectiveness depends on the source-sink structure: Simulation results
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• Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions