LOG-STABLE DISTRIBUTION AND INTERMITTENCY OF TURBULENCE

The logarithm of the breakdown coefficient epsilon-r/epsilon-l, epsilon-r being the mean energy dissipation rate averaged over a sphere of radius r is shown, under a similarity assumption, to obey a stable distribution, the characteristic function of which is given by phi-(z\r/l) = (r/l)(mu/2-alpha - 2)[i z-(ze(i-pi/2))alpha], where mu > 0 and 0 < alpha-less-than-or-equal-to 2. The scaling exponent of the p-th order moment of the energy dissipation rate is calculated to be mu-p = mu(p-alpha - p)/(2-alpha - 2), which is in excellent agreement with the experiments (Anselmet et al. 1984) when the intermittency parameter is mu = 0.20 and the characteristic exponent of the distribution is alpha = 1.65. The probability density function of epsilon-r diverges as 1/epsilon-r(- 1n-epsilon-r)alpha + 1 at the origin and decreases as exp [- A (1n-epsilon-r)alpha/(alpha - 1)], where A > 0, as epsilon --> infinity. The present results include the log-normal theory for alpha = 2 and coincide with the prediction of mu-p due to the beta-model in the limit alpha --> 0.