Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics

We reformulate the problem of hydrodynamic turbulence as a heat flow problem. We obtain thus a prediction $${\zeta }_p=\frac{p}{3}-\frac{1}{\ln \kappa }\ln \mathrm{\Gamma }(\frac{p}{3}+1)$$ for the exponents of the structure functions ($<\mathrm{\mid }{\mathrm{\Delta }}_{r}v{\mathrm{\mid }}^p>=r^{{\zeta }_p}$). The meaning of the adjustable parameter $\kappa$ is that when an eddy of size $r$ has decayed to eddies of size $r\mathrm{/}\kappa$ their energies have a thermal distribution. The above formula, with $(\ln \kappa {)}^{-1}=.32\pm .01$ is compatible with experimental data. This agreement lends supports to our physically motivated picture of turbulence.