2022-08-14T12:33:38Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000129682021-03-01T11:14:01ZDiagram Approach to the Nonlinear Expansion Theory of Turbulence乱流の非線形展開理論とダイアグラム大路, 通雄This paper describes the principle and application of the diagram technique recently introduced into the turbulence theory. First, the theoretical background of various approaches to the statistical mechanics of turbulence is briefly reviewed with special reference to the significance of consolidated or nonlinear expansions which retain a strong nonlinearity even in their lower order terms. Next, the construction and the structure of standard diagrams are expounded for steady homogeneous turbulence under a Gaussian random forcing function mainly after Wyld-Lee's scheme. Three fundamental diagram equations are shown in a consolidated form. They constitute a system of triple integro-differential equations which determines the energy spectrum function, the modified Green's function and the modified vertex function simultaneously. Lastly, known approximate theories such as the cumulant discard, the direct-interaction approximations and Shut'ko's proposal are critically interpreted from the viewpoint of the diagram approach.Article信州大学工学部紀要 33: 55-70 (1972)departmental bulletin paper信州大学工学部1972-12-25application/pdf信州大学工学部紀要3355700037-3818AN00121228https://soar-ir.repo.nii.ac.jp/record/12968/files/Engineering33-06.pdfjpn