A theory of hydrodynamic turbulence based on non-equilibrium statistical mechanics

Abstract

In earlier papers we have studied the turbulent flow exponents ${\zeta }_p$, where $⟨|\Delta \mathbf{v}{|}^p⟩\sim {\ell }^{{\zeta }_p}$ is the contribution to the fluid velocity at small scale $\ell$. Using ideas of non-equilibrium statistical mechanics we have found $${\zeta }_p=\frac{p}{3}-\frac{1}{\ln \kappa }\ln \Gamma (\frac{p}{3}+1)$$ 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.

6 pages

References in corpus (1)

• Non-equilibrium statistical mechanics of turbulence

Cited by in corpus (1)

• Hidden scale invariance in Navier-Stokes intermittency