Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion. IMAGES:

阿韦拉内达（Avellaneda）与马伊达（Majda）在1994年发表于《伦敦皇家学会哲学学报A辑（Philos. Trans. R. Soc. London A）》第346卷第205至233页的研究及多篇早期论文中，报告了湍流扩散的相变现象。该现象可追溯至一项建模假设：湍流流体的能谱在惯性区间内与粘度存在奇异相关性。与之相对，湍流与间歇性的唯象模型则要求，能谱在惯性区间内与粘度无关。若假设能谱符合该唯象模型，则湍流扩散不会出现相变现象。附图：