Passive scalar transport by a non-Gaussian turbulent flow in the Batchelor regime

We analyze passive scalar advection by a turbulent flow in the Batchelor regime. No restrictions on the velocity statistics of the flow are assumed. The properties of the scalar are derived from the statistical properties of velocity; analytic expressions for the moments of scalar density are obtained. We show that the scalar statistics can differ significantly from that obtained in the frames of the Kraichnan model.

Figure 1

Position of the maximum in the $(\xi ,\eta )$ plane as a function of $\alpha$: Gaussian statistics. Straight lines correspond to the boundaries $z_i=0$.

Figure 2

Position of the maximum in the $(\xi ,\eta )$ plane as a function of $\alpha$: Cubic deviation from the Gaussian statistics, (a) $F=-0.1$, (b) $F=0.1$.

Figure 3

The increment $-{\gamma }_{\alpha }$ as a function of the order for the model (33) with $c=2.2$. The dashed curve is the result for the Gaussian distribution which produces the same saturated ${\gamma }_{\alpha }$.