Two Problems in the Statistical Theory of Turbulence

概要

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Two problems in the theory of turbulence are studied by the use of analogy with other areas in theoretical physics. Firstly the problem of determining the probability that a turbulent distribution has a particular velocity U at a point. It is shown that there is an analogy between this problem and a polymer problem, and this reasoning leads to a distribution exp(-U^2/h^<1/3>V^<2/9>) for small U, obtainable by other methods, but exp(-U^<18/7>/(h^<1/3>V^<2/9>)^<18/7>) for large U. The second problem is that of the existence of large fluctuations, the intermittency problem. Here the analogy is with the localized states in a disordered semiconductor, where states exist at negative energies relative to a `mobility edge'. The analogy of these states in turbulence are localized eddies which grow to a size which would be unsuspected in the conventional statistical theories. An eddy of extent α^<-1> and magnitude U grows to a size exp{2γα^<4/3>h^<-1/3>} over a time h^<-1/3>α^<-2/3>, then decays.
理論物理学刊行会の論文
1981-06-10