Simple Model of Intermittent Passive Scalar Turbulence

Abstract

The passive scalar convection by chaotic two-dimensional incompressible flow is studied. Analytically solvable equations are suggested to describe the evolution of the probability density functions of tracer gradients and power spectra. The parameters of the model are expressed explicitly via the correlation functions of the velocity field. The multifractal spectrum f(alpha) of the scalar dissipation field is calculated; strict multifractality holds only for small values of alpha. Stationary and exponentially decaying power spectra of the scalar are obtained.