Nonlocality and intermittency in three-dimensional turbulence

Numerical simulations are used to determine the influence of the nonlocal a nd local interactions on the intermittency corrections in the scaling prope rties of three-dimensional turbulence. We show that neglect of local intera ctions leads to an enhanced small-scale energy spectrum and to a significan tly larger number of very intense vortices ("tornadoes") and stronger inter mittency (e.g., wider tails in the probability distribution functions of ve locity increments and greater anomalous corrections). On the other hand, ne glect of the nonlocal interactions results in even stronger small-scale spe ctrum but significantly weaker intermittency. Thus, the amount of intermitt ency is not determined just by the mean intensity of the small scales, but it is nontrivially shaped by the nature of the scale interactions. Namely, the role of the nonlocal interactions is to generate intense vortices respo nsible for intermittency and the role of the local interactions is to dissi pate them. Based on these observations, a new model of turbulence is propos ed, in which nonlocal (rapid distortion theory-like) interactions couple la rge and small scale via a multiplicative process with additive noise and a turbulent viscosity models the local interactions. This model is used to de rive a simple version of the Langevin equations for small-scale velocity in crements. A Gaussian approximation for the large scale fields yields the Fo kker-Planck equation for the probability distribution function of the veloc ity increments. Steady state solutions of this equation allows one to quali tatively explain the anomalous corrections and the skewness generation alon g scale. A crucial role is played by the correlation between the additive a nd the multiplicative (large-scale) process, featuring the correlation betw een the stretching and the vorticity. (C) 2001 American Institute of Physic s.