Abstract
A study is made of steady homogeneous isotropic turbulence, on the basis of Edwards' Fokker-Planck method introducing the concepts of turbulent diffusion and turbulent viscosity (S.F. Edwards: J. Fluid Mech. 18 (1964) 239). In this paper, the renormalized vertex is introduced in addition to them. The Liouville equation for the probability distribution function is solved, under the requirement that in the perturbative solution, only the leading two terms up to the first order of the renormalized vertex contribute to the second- and third-order velocity correlations. As the result simultaneous nonlinear integral equations are obtained for the turbulent diffusion and viscosity coefficient, and the renormalized vertex. It is shown that these equations are not expected to give Kolmogoroff's spectrum.
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