A simplified Lagrangian 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 wave packets 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 wave packets. 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 these 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)⟩qR⟩, where ⟨E(l,a,r,t)⟩Ris the part of the turbulent energy coming from Fourier components in a band (a−1)karoundk∼l−1, spatially averaged over a volume of sizeR∼l/(a−1) aroundr. ©1995 American Institute of Physics.