Statistical Theory of Passive Scalar Advected by Turbulence: An Application of the Lagrangian Direct-lnteraction Approximation

A closure theory of turbulence so-called the Lagrangian direct-interaction approximation is formulated for a passive scalar field advected by isotropic turbulence. Solutions to the resultant closure equations for the correlation functions of scalar and velocity fields are shown to be completely consistent with well-known phenomenologies on small-scale statistics of turbulence. Keyword: statistical theory of turbulence, direct-interaction approximation, passive scalar field 1. lntroduction We investigate a passive scalar field 0(x, t), e.9., temperature, particle concentration, dye, smoke, etc, which is advected by turbulent velocity field and diffused by molecular diffusion as (1) The velocity field ur(r, t) is governed by the Navier