in intermittent hydrodynamic turbulence

Recent theoretical and numerical results on intermittency in hydrodynamic turbulence and scalar trans-port are described, with special emphasis on the Lagrangian evolution. First, we derive the advected delta-vee system. This simple dynamical system deals with the Lagrangian evolution of two-point velocity and scalar increments in turbulence [1, 2]. It shows that ubiquitous trends of three-dimensional turbulence such as exponential or stretched exponential tails in the probability density functions of transverse velocity incre-ments, as well as negatively skewed longitudinal velocity increments, emerge quite rapidly and naturally from initially Gaussian ensembles. Further extensions of the system are shown to provide simple expla-nations for other known intermittency trends in turbulence: (i) that transverse velocity increments tend to be more intermittent than longitudinal ones, (ii) that in two dimensions, vorticity increments are inter-mittent while velocity increments are not, (iii) that scalar increments typically become more intermittent than velocity increments and, finally, (iv) that velocity increments in four-dimensional turbulence are more intermittent than in three dimensions. 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