Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar

Results of direct numerical simulations (DNS) for the decay of an initially Gaussian field of turbulence convecting a passive scalar are compared with equivalent results for the direct-interaction approximation (DIA) and the test-field model (TFM). The Taylor microscale Reynolds number R λ and the equivalent Péclet number P λ of the comparison ranged from 20–8 and 10–4, respectively. The Prandtl number Pr equals 0·5. Our results show a satisfactory agreement of both theories and numerical simulations, with the DIA giving better overall agreement, especially at small scales. This improved small-scale agreement - which appears to hold up to R λ ≃ 30 - is related to the relatively long coherence times of the small scales, and to the fact that the TFM, containing as it does a built-in compliance to the fluctuation dissipation theorem, cannot properly cope with this fact. We also give a comparison of results for the velocity skewness with the experiments of Tavoularis, Bennett & Corrsin (1978).