Energy dissipation rate in the inertial sublayer of turbulent channel flow at large but finite Reτ

Abstract

A theory of the position dependence of the statistical average of the energy dissipation rate per unit mass ($ϵ$>) in the inertial sublayer of turbulent channel flow is proposed on the basis of the spirit of the Linear Response Theory (LRT) of turbulence. The theory with data consisting of a series of direct numerical simulations up to Re${}_{\ensuremath{\tau}}\ensuremath{\approx}$ 8000 suggests ${\ensuremath{\kappa}}_{ϵ}\ensuremath{\approx}$ 0.44 for the von K\'arm\'an constant of $ϵ$>.