Abstract
As the first stage of developments of our statistical theory of turbulence, fundamental aspects of the similarity laws are investigated through the three cases of isotropic turbulence (A), turbulent wake (B) and turbulent boundary layer (C). In (A), it is first interpreted as the essential character of shearless turbulence that the distribution function F 0 ( u , v , w ) takes the form of Gauss function without correlation. Next, the hypothesis of isotropic turbulence due to G. I. Taylor is proved to hold in the case of shearless turbulence with a uniform mean velocity distribution. Then, the hypothesis of similarity preservation introduced first by Karman-Howarth is derived as one of our theoretical result under the supposition of ideal state. Under this supposition we get the diffusion law \(L^{2}{\nbacksim}t\). The decay law in the initial period \(\textbf{\itshape u}^{2}{\nbacksim}t^{-1}\) is derived by taking the vortex chaos motion of α=1. Further, some interpretations are made on the problem of ene...
Published Version
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