TURBULENT-DIFFUSION PHASE-TRANSITION IS DUE TO SINGULAR ENERGY-SPECTRUM

The phase transition for turbulent diffusion, reported by Avellaneda a nd Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Sec. London A 346, 205-233, and several earlier papers], is traced to a mod eling assumption in which the energy spectrum of the turbulent fluid i s singularly dependent on the viscosity in the inertial range. Phenome nological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inert ial range. When the energy spectrum is assumed to be consistent with t he phenomenological models, there is no phase transition for turbulent diffusion.