Comparison of methods for calculating turbulent diffusion coefficients

Different methods for calculating the turbulent diffusion coefficient DT of a passive scalar impurity in an infinite homogeneous isotropic stationary turbulent medium are examined. The values of DT calculated by these methods are compared for two limiting types of turbulence, viz., turbulence with a δ-function spectrum and turbulence with a Kolmogorov-type spectrum. The temporal dependence of the velocity correlators is assumed to be exponential. It is shown that the most accurate method is based on the use of the solution of the nonlinear equation for the averaged Green’s function with consideration of the contribution from the four-point turbulent velocity correlators. A comparison with the results of other methods that are simpler from the mathematical standpoint shows that some of them also permit the calculation of DT with relatively good accuracy.