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 $ζ_p={p\over3}-{1\over\lnκ}\lnΓ({p\over3}+1)$ for the exponents of the structure functions ($<|Δ_rv|^p>=r^{ζ_p}$). The meaning of the adjustable parameter $κ$ is that when an eddy of size $r$ has decayed to eddies of size $r/κ$ their energies have a thermal distribution. The above formula, with $(\lnκ)^{-1}=.32\pm.01$ is compatible with experimental data. This agreement lends supports to our physically motivated picture of turbulence.

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