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Prog. Theor. Phys. Vol. 70 No. 5 (1983) pp. 1183-1196
Intermittency and Relative Diffusion in Fully-Developed Turbulence
Hazime Mori and
Kiyofumi Takayoshi
Department of Physics, Kyushu University 33, Fukuoka 812
(Received February 21, 1983; Revised June 20, 1983)
Abstract:
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 paire of particles at time t is asymptotically given by L*2(t) ∼tψ 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 = log2 (21+a0 -1) with a0 = 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 Bénard convection, a= (2+ µ)/5, µ\doteqdot0.261 ≃1/4 and ψ\doteqdot10.5. For the 3d helicity cascade, a=(1+ µ)/3, µ\doteqdot0.203 ≃1/5 and ψ\doteqdot10.1. 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.
URL :
http://ptp.ipap.jp/link?PTP/70/1183/
DOI : 10.1143/PTP.70.1183
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