On how a joint interaction of two innocent partners (smooth advection and linear damping) produces a strong intermittency

Abstract

Forced advection of passive scalar by a smooth d-dimensional incompressible velocity in the presence of linear damping is studied. Acting separately advection and damping do not lead to an essential intermittency of the steady scalar statistics, while being mixed together produce a very strong non-Gaussianity in the convective range: 2n-th moment of scalar difference, 〈[θ(t;r)−θ(t;0)]2n〉 is proportional to rξ2n, ξ2n=min{2n,d2/4+2αdn/[(d−1)D]−d/2}, where α/D measures the rate of the damping in the units of the stretching rate. The probability density function (PDF) of the scalar difference is also found.