Passive scalar spectrum in isotropic turbulence: Prediction by the Lagrangian direct-interaction approximation

Abstract

The Lagrangian direct-interaction approximation developed previously by the present authors [S. Kida and S. Goto, J. Fluid Mech. 345, 307 (1997)] is applied to a passive scalar field in isotropic turbulence. We examine the behavior of solutions to the resultant closure equations for the correlation function of the scalar field for arbitrary values of the Schmidt number, and show systematically that the solutions are completely consistent with the phenomenological theories on the scalar spectral function by Obukhov (1949), Corrsin (1951), Batchelor et al. (1959), and Batchelor (1959). The universal forms of the function in the statistically stationary state are obtained by solving the closure equations numerically in the whole wave number range for each case of moderate, extremely large, and small values of the Schmidt number.