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

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Abstract
This paper applies the test field model developed by Kraichnan to the study of an isotropic, passive scalar contaminant convected by decaying isotropic turbulence. Test field model predictions of scalar and velocity dissipation spectra at large Reynolds and Péclet numbers are shown to be in excellent agreement with atmospheric data, after intrinsic scale constants in the model are adjusted to give valid inertial range coefficients. Theoretical values for the inertial range coefficients are obtained for large and small Prandtl numbers. Simulation results for velocity and scalar energy, dissipation and transfer spectra and second- and third-order velocity, scalar and velocity–scalar correlations at moderate Reynolds and Péclet numbers are shown to agree moderately well with heated grid turbulence data. Simulation results are presented for the normalized decay rates of the scalar and velocity dissipation rates and for the ratio of the velocity to scalar decay time scales; these quantities are employed in second-order modelling. In the self-similar decay mode the simulations yield unity levels of the normalized decay rates and of the ratio of decay time scales over the moderate range of Reynolds and Prandtl numbers investigated. These results are compared with data from heated grid turbulence experiments and are discussed in the light of asymptotic decay of concomitant scalar and velocity fields.