**Intermittency trends and Lagrangian evolution of
non-Gaussian statistics in**

**turbulent flow and scalar transport**

Charles Meneveau

Department of Mechanical Engineering and Center of

Environmental and Applied Fluid Mechanics, The Johns Hopkins

University, Baltimore, MD, 21218

The Lagrangian evolution of two-point velocity and scalar increments in turbulence is considered, based on the "advected delta-vee system” (Li & Meneveau, Phys. Rev. Lett. 2005). This system has already been used to show that ubiquitous trends of 3D turbulence such as exponential or stretched exponential tails in the probability density functions of transverse velocity increments, as well as negatively skewed longitudinal velocity increments, emerge quite rapidly and naturally from initially Gaussian ensembles. In this paper, the approach is extended to provide simple explanations for other known intermittency trends in turbulence: (i) that transverse velocity increments tend to be more intermittent than longitudinal ones, (ii) that in 2D turbulence, vorticity increments are intermittent while velocity increments are not, (iii) that scalar increments typically become more intermittent than velocity increments and, finally,

(iv) that velocity increments in 4D turbulence are more intermittent than in 3D turbulence. While the origin of these important trends can thus be elucidated qualitatively, predicting quantitatively the statistically steady-state levels and dependence on scale remains an open problem that would require including the neglected effects of pressure, inter-scale interactions and viscosity.