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 d. Anomalous scaling exponent of the 2n-th scalar's structural function is found analytically.
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