A Statistical Approach to Steady Homogeneous Isotropic Turbulence, Based on Edwards’ FokkerPlanck Method
Abstract
A study is made of steady homogeneous isotropic turbulence, on the basis of Edwards’ FokkerPlanck 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 thirdorder 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.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 October 1975
 DOI:
 10.1143/JPSJ.39.1100
 Bibcode:
 1975JPSJ...39.1100Y
 Keywords:

 FokkerPlanck Equation;
 Homogeneous Turbulence;
 Isotropic Turbulence;
 Statistical Analysis;
 Apexes;
 Integral Equations;
 Nonlinear Equations;
 Probability Distribution Functions;
 Steady Flow;
 Turbulent Diffusion;
 Viscosity;
 Fluid Mechanics and Heat Transfer