A closure theory of intermittency of turbulence

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Abstract
The variational approach to the closure problem of turbulence theory, proposed in an earlier article [Phys. Fluids 2 6, 2098 (1983); 2 7, 2229 (1984)], is extended to evaluate the flatness factor, which indicates the degree of intermittency of turbulence. Since the flatness factor is related to the fourth moment of a turbulent velocity field, the corresponding higher‐order terms in the perturbation solution of the Liouville equation have to be considered. Most closure methods discard these higher‐order terms and fail to explain the intermittency phenomenon. The computed flatness factor of the idealized model of infinite isotropic turbulence ranges from 9 to 15 and has the same order of magnitude as the experimental data of real turbulent flows. The intermittency phenomenon does not necessarily negate the Kolmogorov k−5/3 inertial range spectrum. The Kolmogorov k−5/3 law and the high degree of intermittency can coexist as two consistent consequences of the closure theory of turbulence. The Kolmogorov 1941 theory [J. Fluid Mech. 6 2, 305 (1974)] cannot be disqualified merely because the energy dissipation rate fluctuates.