A closure model for intermittency in three dimensional incompressible turbulence

A simplified Lagrangean closure for the Navier-Stokes equation is used to study the production of intermittency in the inertial range of three dimensional turbulence. This is done using localized wavepackets following the fluid rather than a standard Fourier basis. In this formulation, the equation for the energy transfer acquires a noise term coming from the fluctuations in the energy content of the different wavepackets. Assuming smallness of the intermittency correction to scaling allows the adoption of a quasi-gaussian approximation for the velocity field, provided a cutoff on small scales is imposed and a finite region of space is considered. In this approximations, the amplitude of the local energy transfer fluctuations, can be calculated self consistently in the model. Definite predictions on anomalous scaling are obtained in terms of the modified structure functions: << E(l, a) >R>, where < E(l, a, r, t) >R is the part of the turbulent energy coming from Fourier components in a band (a − 1)k around k ∼ l, spatially averaged over a volume of size R ∼ l a−1 around r. PACS numbers 47.27. -i Submitted to Physics of Fluids, 11-15-1994