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

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, $<\mathrm{\mid }\theta (t;\mathbf{r})-\theta (t;0){\mathrm{\mid }}^q>$ is proportional to $r^{{\xi }_q}$, $\xi _{q}=\sqrt{d^{2}/4+\alpha dq/[ (d-1)D]}-d/2$,where$\alpha /D$ measures the rate of the damping in the units of the stretching rate. Probability density function (PDF) of the scalar difference is also found.