Two Problems in the Statistical Theory of Turbulence

S. F. Edwards
1980 Progress of Theoretical Physics Supplement  
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 (- for large U. The second problem is that of the existence of large fluctuations, the intermittency problem. Here the analogy is with
more » ... 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 a·• and magnitude U grows to a size exp {2ra' 18 h-118 } over a time h" 118 a·' 18 , then decays.
doi:10.1143/ptps.69.1 fatcat:7v5xa7w7kjh63fz6dqtdx54vye