Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics

Abstract

We reformulate the problem of hydrodynamic turbulence as a heat flow problem. We obtain thus a prediction $${\zeta }_p=\frac{p}{3}-\frac{1}{\ln \kappa }\ln \Gamma (\frac{p}{3}+1)$$ for the exponents of the structure functions ($<|{\Delta }_{r}v{|}^p>=r^{{\zeta }_p}$). The meaning of the adjustable parameter $\kappa$ is that when an eddy of size $r$ has decayed to eddies of size $r/\kappa$ 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.

6 pages

References in corpus (2)

• Energy transfer in a fast-slow Hamiltonian system
• A mechanical model for Fourier's law of heat conduction

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