A local energy-transfer theory of isotropic turbulence

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Abstract
It is shown that a nonlinear integral equation for turbulent energy transport may be reinterpreted in terms of a Heisenberg-type effective viscosity. A new equation is derived for the effective viscosity. This is found to permit general expansions of the integral kernels, in powers of wavenumber ratios, leading to local (differential) equations for the energy spectrum and effective viscosity. It is found that these equations yield the Kolmogoroff distribution as the inertial-range solution, and that the numerical predictions agree quite well with experimental results. The final equations are similar to equations recently derived by Nakano (1972), and the relationship between the two theories is discussed.

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