Abstract-
We consider turbulent mixing of a passive scalar in the presence
of a mean scalar gradient, with an emphasis on the resulting mean scalar
flux. The effect of the Schmidt number, defined as the ratio of viscosity
to diffusivity, is also taken into account.
The velocity-scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to limit the possible contribution of the sub-Kolmogorov scales to the scalar flux at high Schmidt number. At low Schmidt number we derive a new asymptotic result for the cospectrum in the inertial-diffusive range. The sparse direct-interaction perturbation (SDIP), the stretched-spiral vortex model, and direct numerical simulation (DNS) at a Taylor Reynolds number of 265 were each used to calculate the cospectrum, and a comparison is made with experiment at a Schmidt number of 0.7.
The stretched-spiral vortex model was also used to derive expressions for the modal time correlation functions of the velocity and scalar fields. Winding by the vortex core is shown to lead to an inertial time scale, and movement of the vortex structures by the large scale flow leads to a sweeping time scale. Comparison is made with results from DNS.
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