In this Rapid Communication, we study the behavior of a strongly diffusive passive scalar field $T$ submitted to a freely decaying, homogeneous and isotropic turbulence with eddy-damped quasinormal Markovian simulations. We present a new subrange located between the $k^{-17/3}$ inertial-diffusive subrange and the Kolmogorov wave number $k_{\eta }$. This subrange is generated by small-scale convection linked to $k_{\eta }$ that balances diffusion effects. Thus, we build a typical length scale $k_{CD}^{-1}$ based on convection and diffusion and give an expression for the shape of the passive scalar spectrum in this subrange $E_T\sim \sqrt{Pr}{k}^{-11/3}$ using physical arguments. This result unifies two different theories coming from Batchelor [G. K. Batchelor, J. Fluid. Mech. 5, 113 (1959)] and Chasnov [J. Chasnov et al., Phys. Fluids A 1, 1698 (1989)] and explains results previously obtained experimentally.

• Received 4 September 2014

DOI:https://doi.org/10.1103/PhysRevE.91.011001