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Non-locality and Intermittency in 3D Turbulence

J. -P. Laval·B. Dubrulle·S. Nazarenko
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Abstract

Numerical simulations are used to determine the influence of the non-local and local interactions on the intermittency corrections in the scaling properties of 3D 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. On the other hand, neglect of the non-local interactions results in even stronger small-scale spectrum but significantly weaker intermittency. Based on these observations, a new model of turbulence is proposed, in which non-local (RDT-like) interactions couple large and small scale via a multiplicative process with additive noise and the local interactions are modeled by a turbulent viscosity. This model is used to derive a simple toy 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 to qualitatively explain the anomalous corrections and the skewness generation along scale.

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J. -P. Laval, B. Dubrulle, S. Nazarenko. 2001-01-05. Non-locality and Intermittency in 3D Turbulence. https://doi.org/10.1063/1.1373686

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