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

David Ruelle

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.