The Structure of Isotropic Turbulence At Very High Reynolds Numbers
The Structure of Isotropic Turbulence At Very High Reynolds Numbers
R H Kraichnan
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As the inequalities k « k « R. K become stronger, the range of t about the origin in which wholly local contributions dominate becomes a smaller fraction of (v k)" . - 31 - 7. 2. Behavior for k » k Let us suppose that R is sufficiently large that there are values of k, very large compared to k, for which (7. 1) is still valid. There appear to be two general possibilities for the energy supply to such wavenumbers. Either they are powered by an essentially local cascade process, or they draw powe...r principally from wavenuinbers, the order of k, in the ref^ion where the spectrum begins to fall below the inertial range form. We might perhaps anticipate that the first possibility is the actual fact. In the inertial range we have seen that the energy transport is essentially local. Let us now imagine a part of the spectrum to be depressed by local viscous drain. It would appear that the net input from much lower wavenumbers should be affected relatively little, since to start with the local region was already very far fixsm equipartition with these wavenumbers.
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