Strong effect of weak diffusion on scalar turbulence at large scales

M. Chertkov; I. Kolokolov; V. Lebedev

doi:10.1063/1.2793145

paper

Strong effect of weak diffusion on scalar turbulence at large scales

arXiv:0706.2928 · doi:10.1063/1.2793145

Abstract

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$ , injection scale, $l$ , and diffusive scale, $r_{d}$ . The scales are well separated if the diffusivity is small, $r_{d} ≪ l, L$ , and one normally says that effects of diffusion are confined to smaller scales, $r ≪ r_{d}$ . However, if the velocity is single scale one finds that a weak dependence of the scalar correlations on the molecular diffusivity persists to even larger scales, e.g. $l ≫ r ≫ r_{d}$ \cite{95BCKL}. We consider the case of $L ≫ l$ and report a counter-intuitive result -- the emergence of a new range of large scales, $L ≫ r ≫ l^{2} / r_{d}$ , where the diffusivity shows a strong effect on scalar correlations.

4 pages, 1 figure, submitted to Physics of Fluids

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Growing condensate in two-dimensional turbulence