Abstract
The Dyson equations of Martin et al. [Phys. Rev. A 8, 423 (1973)] are truncated after the first non-Gaussian correction, yielding Kraichnan’s direct interaction approximation [J. Fluid Mech. 5, 497 (1959)], and the self-similarity of the inertial range is used to reduce the number of independent variables. Yakhot and Orszag’s result [J. Sci. Comput. 1, 3 (1986)] is recovered by expanding these equations in the parameter ε, which measures the departure of the energy-spectrum exponent from one. In making this expansion, only certain nonlocal, eddy-viscosity-like interactions are retained at first order; all other interactions are relegated to higher orders. As a result, the expansion fails to notice that the direct interaction approximation gives the incorrect energy-spectrum exponent.
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