In earlier papers, we have studied the turbulent flow exponents
\(\zeta _p\), where
\(\langle |\Delta \mathbf{v}|^p\rangle \sim \ell ^{\zeta _p}\) and
\(\Delta \mathbf{v}\) is the contribution to the fluid velocity at small scale
\(\ell \). Using ideas of non-equilibrium statistical mechanics we have found
$$\begin{aligned} \zeta _p={p\over 3}-{1\over \ln \kappa }\ln \Gamma \left( {p\over 3}+1\right) \end{aligned}$$
where
\(1/\ln \kappa \) is experimentally
\(\approx \,0.32\,\pm \,0.01\). The purpose of the present note is to propose a somewhat more physical derivation of the formula for
\(\zeta _p\). We also present an estimate
\(\approx \,100\) for the Reynolds number at the onset of turbulence.