Repeated Cascade Theory of Homogeneous Turbulence
Semi-annual technical rept. Jul-Dec 1971
CITY COLL RESEARCH FOUNDATION NEW YORK
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The problem of turbulent spectrum engenders two coupled hierarchies one originates from the development of stress. Leading to a transfer function, and the other from the development of an eddy viscosity. In order to incorporate physical roles among scales, the turbulent velocity fluctuation is decomposed into a series of ranks in the increasing order of randomness, contributing successively to energy or stress, eddy viscosity, relaxation frequency, and higher rank frequencies in the memory chain. As a result, the first hierarchy mentioned above becomes closed at the quadruple correlation. The second hierarchy governs the eddy viscosities of different ranks, related to relaxation frequencies of such ranks, in the form of a memory chain. It is cut off by an implicit viscous mechanism.
- Fluid Mechanics