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, $$ 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.Comment: 4 pages, RevTex, Submitted to Phys. Fluid

Anomalous Scaling Exponents of a White-Advected Passive Scalar

For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality $d\gg1$ is considered. Scaling exponents of the scalar field are analytically found to be $\zeta_{2n}=n\zeta_2-2(2-\zeta_2)n(n-1)/d$, while those of the dissipation field are $\mu_{n}=-2(2-\zeta_2)n(n-1)/d$ for orders $n\ll d$. The refined similarity hypothesis $\zeta_{2n}=n\zeta_2+\mu_{n}$ is thus established by a straightforward calculation for the case considered.Comment: 4 pages, RevTex 3.0, Submitted to Phys. Rev. Let

Non-universality of the scaling exponents of a passive scalar convected by a random flow

We consider passive scalar convected by multi-scale random velocity field with short yet finite temporal correlations. Taking Kraichnan's limit of a white Gaussian velocity as a zero approximation we develop perturbation theory with respect to a small correlation time and small non-Gaussianity of the velocity. We derive the renormalization (due to temporal correlations and non-Gaussianity) of the operator of turbulent diffusion. That allows us to calculate the respective corrections to the anomalous scaling exponents of the scalar field and show that they continuously depend on velocity correlation time and the degree of non-Gaussianity. The scalar exponents are thus non universal as was predicted by Shraiman and Siggia on a phenomenological ground (CRAS {\bf 321}, 279, 1995).Comment: 4 pages, RevTex 3.0, Submitted to Phys.Rev.Let