Passive Scalar Diffusion in Two Dimensional Turbulence in the Lagrangian Renormalized Approximation

Abstract

Passive scalar diffusion in two dimensional turbulence is considered on the basis of Lagrangian renormalized approximation. The probability density function for particle pair dispersion is found to be selfsimilar in the energy cascading range and to be lognormal in both the enstrophy and the viscous convective ranges. The spectrum F ( k ) of scalar fluctuations is found to be F ( k )= C s χ e -1/3 k -5/3 with C s =0.198 in the energy cascading range, F ( k )= C ' s χβ -1/3 k -1 {ln( k / k I )} -1/3 with C ' s =0.561 in the enstrophy cascading range, \(F(k){=}{\sqrt{6}}{\chi}({\nu}/{\varepsilon})^{1/2}k^{-1}\) in the viscous convective range and F ( k )'s in other ranges are also shown. It is shown that in the enstrophy inertial range the turbulent diffusivity is dominated by large scale eddies. The evolution of the mean square distance of the particle pair is compared with the data of ballon release experiments by Er-El and Peskin (J. Atmos. Sci. 38 2264 (1981)).