Batchelor’s spectrum from an axisymmetric strained scalar field

The Pullin and Lundgren [Phys. Fluids 13, 2553 (2001)] model of passive scalar transport together with an axisymmetric solution of the advection diffusion equation is used to model the scalar variance spectrum in the viscous-convective subrange. When the Schmidt number is large, the resulting spectrum shows k(-1) scaling before an ultimate diffusive cutoff, in agreement with Batchelor's [J. Fluid Mech. 5, 113 (1959)] earlier result. The present analysis shows how the k(-1) range gradually emerges as the Schmidt number is steadily increased, and it provides an estimate of the Batchelor constant q(B)=2 root 15. This value, which depends on assumptions discussed within the paper, is large compared to most other theoretical, experimental, and numerical results.