Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics

TL;DR

This paper models hydrodynamic turbulence as a heat flow problem, deriving a formula for structure function exponents that aligns well with experimental data, supporting a thermodynamic perspective on turbulence.

Contribution

It introduces a novel reformulation of turbulence as a heat flow problem, providing a predictive formula for structure function exponents based on thermodynamic principles.

Findings

Derived a formula for structure function exponents in turbulence.

Predicted exponents are consistent with experimental data.

Supported a thermodynamic interpretation of turbulence phenomena.

Abstract

We reformulate the problem of hydrodynamic turbulence as a heat flow problem. We obtain thus a prediction $$ \zeta_p={p\over3}-{1\over\ln\kappa}\ln\Gamma({p\over3}+1) $$ for the exponents of the structure functions ($<|\Delta_rv|^p>=r^{\zeta_p}$). 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.