The direct-interaction approximation for turbulence maintained by stationary, isotropic, random stirring forces is formulated in the wavenumber-frequency domain. Further, simplifying approximations are made. The final equations involve the wavenumber energy-spectrum, a characteristic correlation frequency for each wavenumber, and a characteristic response frequency for each wavenumber. A relation is exhibited between the simplified equations and a Fokker-Planck type approximation recently proposed by Edwards.
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Robert H. Kraichnan (1964) studied this question.
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