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

Abstract

Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping 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: $q$-th (positive) moment of the absolute value of scalar difference, $<|θ(t;{\bf r})-θ(t;0)|^{q}> $ is proportional to $r^{ξ_{q}}$, $ξ_{q}=\sqrt{d^{2}/4+αdq/[ (d-1)D]}-d/2$, where $α/D$ measures the rate of the damping in the units of the stretching rate. Probability density function (PDF) of the scalar difference is also found.