Instanton for random advection

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 $n\gg d$\mathrm{.}Anomalousscalingexponentofthe$2n$-th scalar’s structural function is found analytically.