Statistical theory of passive scalar turbulence within the viscous-convective range

Passive scalar turbulence in the viscous-convective range is investigated via a self-consistent closure theory. Without relying on any empirical parameter the theory successfully explained the scalar-variance spectrum proportional to the inverse wavenumber k^-1 from the scalar's deformation timescale dominated by the Kolmogorov-scale eddy, which agrees with the physical viewpoint of Batchelor (1959). High Schmidt number (Sc) calculations up to Sc=100000 suggest that a clear Batchelor spectrum may appear in k00exη1 for S00exc10000 where η is the Kolmogorov length.