The structure of isotropic turbulence at very high Reynolds numbers

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Abstract
A recapitulation is first given of a recent theory of homogeneous turbulence based on the condition that the Fourier amplitudes of the velocity field be as randomly distributed as the dynamical equations permit. This theory involves the average infinitesimal-impulse-response functions of the Fourier amplitudes and employs a new kind of perturbation method which yields what are belived to be exact expansions of third- and higher-order statistical moments of the Fourier amplitudes in terms of second-order moments and these response functions.In the present paper the theory is applied in lowest approximation (called the direct-interaction approximation) to stationary isotropic turbulence of very high Reynolds number. The characteristic wave-number where An is a universal constant.The theory is compared with experiment and is found to be slightly better supported than the Kolmogorov theory. However, it is stressed that extreme caution must be exercised in interpreting the experimental evidence as support for either theory.An analysis is given of the relations between the Kolmogorov theory, Heisen-berg's heuristic theory, the analytical theories of Heisenberg and Chandrasekhar, the theories of Proudman & Reid and Tatsumi, and the present theory.

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