Fusion rules and conditional statistics in turbulent advection

Fusion rules in turbulence address the asymptotic properties of many-point correlation functions when some of the coordinates are very close to each other. Here we put to the experimental test some nontrivial consequences of the fusion rules for scalar correlations in turbulence. To this aim we examine passive turbulent advection as well as convective turbulence. Adding one assumption to the fusion rules, one obtains a prediction for universal conditional statistics of gradient fields. We examine the conditional average of the scalar dissipation field $〈{\nabla }^{2}T\left(\mathrm{r}\right)\left|T\right(\mathrm{r}+\mathrm{R})-T(\mathrm{r})〉$ for $R$ in the inertial range and find that it is linear in $T(\mathrm{r}+\mathrm{R})-T\left(\mathrm{r}\right)$ with a fully determined proportionality constant. The implications of these findings for the general scaling theory of scalar turbulence are discussed.