Log-Stable Distribution and Intermittency of Turbulence

The logarithm of the breakdown coefficient e r /e l , e 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 ϕ( z | r / l )=( r / l ) (µ/2 α -2)[i z -( z e $ i π/2 ) α ] , where µ>0 and 0 0, as e→∞. The present results include the log-normal theory for α=2 and coincide with the prediction of µ p due to the β-model in the limit α→0.