The inertial-range spectrum from a local energy-transfer theory of isotropic turbulence

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Abstract
It has been shown previously that a nonlinear integral equation for turbulent energy transport could be re-interpreted in terms of a Heisenberg-type effective viscosity. The resulting integral equations were used to derive local (differential) equations for the energy spectrum and effective viscosity. The author considers the integral formulation of the theory and restrict his attention to the inertial range of wavenumbers. It is shown that the equations yield the Kolmogoroff distribution, in the limit of infinite. Reynolds numbers. The Kolmogoroff spectrum constant is calculated and found to be alpha =2.5 which is marginally outside the experimental range. It is argued that this result is sufficient encouragement to develop a time-dependent form of the theory, which would allow a more decisive comparison with experiment.

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