# Tentative: Seminar, David Ruelle (IHES, France), A Theory of Hydrodynamic Turbulence Based on Non-Equilibrium Statistical Mechanics

## Date:

Tuesday, April 5, 2022, 9:30am

## Location:

Jefferson 356

Title: 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 $$\langle|\Delta{\bf v}|^p\rangle\sim\ell^{\zeta_p}$$ and $$\Delta{\bf v}$$ is the contribution to the fluid velocity at small scale $$\ell$$. Using ideas of non-equilibrium statistical mechanics we have found
$$\zeta_p={p\over3}-{1\over\ln\kappa}\ln\Gamma({p\over3}+1)$$ where $$1/\ln\kappa$$ is experimentally $$\approx0.32\pm0.01$$.  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 $$\approx100$$ for the Reynolds number at the onset of turbulence.