Nonlocality and intermittency in three-dimensional turbulence

Numerical simulations are used to determine the influence of the nonlocal and local interactions on the intermittency corrections in the scaling properties of three-dimensional turbulence. We show that neglect of local interactions leads to an enhanced small-scale energy spectrum and to a significantly larger number of very intense vortices ("tornadoes") and stronger intermittency (e.g., wider tails in the probability distribution functions of velocity increments and greater anomalous corrections). On the other hand, neglect of the nonlocal interactions results in even stronger small-scale spectrum but significantly weaker intermittency. Thus, the amount of intermittency 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 responsible for intermittency and the role of the local interactions is to dissipate them. Based on these observations, a new model of turbulence is proposed, in which nonlocal (rapid distortion theory-like) interactions couple large and small scale via a multiplicative process with additive noise and a turbulent viscosity models the local interactions. This model is used to derive a simple version of the Langevin equations for small-scale velocity increments. A Gaussian approximation for the large scale fields yields the Fokker-Planck equation for the probability distribution function of the velocity increments. Steady state solutions of this equation allows one to qualitatively explain the anomalous corrections and the skewness generation along scale. A crucial role is played by the correlation between the additive and the multiplicative (large-scale) process, featuring the correlation between the stretching and the vorticity. (C) 2001 American Institute of Physics