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- W1977798907 abstract "In the moment formulation, the direct-interaction approximation equations have been derived by developing perturbation about three different states: the laminar flow (Wyld), a turbulent flow (Kraichnan), and the Gaussian random process (Phythian). Along the parallel line, the pertubation theories in the distribution function formulation have also been developed about the same three states: the laminar flow (Balescu-Senatorski), a turbulent flow (Herring), and the Gaussian random process (Edwards). Herring's modal energy and averaged Green's equations are the basic turbulence equations of the distribution function formalism. The modal energy equation, however, represents the simultaneous-time limit of Kraichnan's covariance equation. This paper provides a unified statistical mechanical framework for the three turbulence theories of the distribution function formalism. We have first revised the derivation of Balescu and Senatorski and then presented an alternate method for Herring's self-consistent-field approximation in terms of the action-angle variables. Finally, we have shown that Edwards' theory cannot give the totally correct stationary dynamics because it is not possible to uniquely determine the dynamic friction and diffusion coefficient in the distribution function formulation." @default.
- W1977798907 created "2016-06-24" @default.
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- W1977798907 date "1974-09-01" @default.
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- W1977798907 title "Statistical mechanical approaches to fluid turbulence" @default.
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- W1977798907 doi "https://doi.org/10.1063/1.1666849" @default.
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