A test field model study of a passive scalar in isotropic turbulence

The test field model is applied to the decay of a passive scalar convected by homogeneous turbulence. The accuracy of the theory is first assessed by comparing its predictions to experiments for a range of Reynolds and Prandtl numbers. The decay of an initially random scalar field injected into a preexisting field of turbulence is then studied. The goal is to understand the dependence of velocity and scalar time scales on their respective energy spectra, paralleling - insofar as possible - the recent experimental study of Warhaft and Lumley (1978). The results agree reasonably well with the trends predicted by the experiments. As in the experimental results, for certain initial conditions, an anomalous scalar 'inertial range' is found. The theoretical results appear consistent with the interpretation that these cases have a higher scalar Reynolds number than those without an anomaly.