Lognormal intermittency model
= Lognormal intermittency model
{title2=$\zeta_p=p/3-\mu p(p-3)/18$}
If $\log(\epsilon_r/\epsilon)$ is Gaussian with <variance> $\sigma_r^2$, normalization gives $\langle\epsilon_r^q\rangle/\epsilon^q=\exp[q(q-1)\sigma_r^2/2]$. Taking $\exp(\sigma_r^2)=B(\ell/r)^\mu$ predicts $\zeta_p=p/3-\mu p(p-3)/18$. Its eventual negative high-order exponents show that this extrapolation cannot hold for arbitrarily large orders with finite uniform velocity <moments>.