Approximations for Steady-State Isotropic Turbulence

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Abstract
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.