Intermittency and Relative Diffusion in Fully-Developed Turbulence

概要

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A general formula for the intermittency exponent μ is proposed to explore various normal cascades in a unified manner. The mean vorticity amplitude ω(l) of eddies of length scale l obeys an inverse-power law ω(l)〜l^<-a> with 1>a≧0. The mean square L_*^2(t) of the relative distance of a pair of particles at time t is asymptotically given by L_*^2(t)〜t^ψ with ψ=2/(a-μ) for L_*(t)≫L_*(0). It is shown that Fujisaka and Mori's variational principle of maximizing an information entropy of intermittency leads to μ+a=log_2(2^<1+a_0>-1) with a_0=a(μ=0). For the three-dimensional energy cascade for which a=(2+μ)/3, this leads to μ 0.341⋍1/3 and ψ 4.56 in accordance with the previous results by Fujisaka, Takayoshi and Mori. This is consistent with experimental values of μ and ψ. For the 2d enstrophy cascade, a=μ/3, μ=0 and L_*^2(t)=L_*^2(0)exp(At) with a positive constant A in agreement with experiments on μ and L_*^2(t). For the Benard convection, a=(2+μ)/5, μ≒0.261⋍1/4 and ψ≒10.5. For the 3d helicity cascade, a=(1+μ)/3, μ≒0.203⋍1/5 and ψ≒10.1. Critical exponents of the inviscid singularities of generalized enstrophies are also determined. A modification of the vortex stretching and the relative diffusion in decaying turbulence is also discussed.
理論物理学刊行会の論文
1983-11-25