Interacting scales and energy transfer in isotropic turbulence

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Abstract
The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far‐dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far‐dissipation range is found to be dominated by relatively nonlocal interactions, supporting the classical notion that the far‐dissipation range is slaved to the Kolmogorov scales. The measured energy transfer is compared with the classical models of Heisenberg [Z. Phys. 124, 628 (1948)], Obukhov [Isv. Geogr. Geophys. Ser. 13, 58 (1949)] and the more detailed analysis of Tennekes and Lumley [The First Course of Turbulence (MIT Press, Cambridge, MA, 1972)]. The energy transfer statistics measured in the numerically simulated flows are found to be nearly self‐similar for wave numbers in the inertial range. Using the self‐similar form measured within the limited scale range of the simulation, an ‘‘ideal’’ energy transfer function and the corresponding energy flux rate for an inertial range of infinite extent are constructed. From this flux rate the Kolmogorov constant is calculated to be 1.5, in excellent agreement with experiments [A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2].

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