Similarity for dissipation-scaled wall turbulence

Abstract

In this paper, we put forward a hypothesis for turbulent kinetic energy, Reynolds stresses and scalar variance in wall-bounded turbulent flows, whereby these quantities, when normalized with the kinematic viscosity, mean turbulent energy dissipation rate and scalar dissipation rate, are independent of the Reynolds and Péclet numbers when they are sufficiently large. In particular, there exist two scaling ranges: (i) an inertial-convective range at sufficiently large distance from the wall over which a $2/3$ power-law scaling emerges for all quantities mentioned above; (ii) a viscous-convective range between the viscous-diffusive and inertial-convective ranges at large Prandtl number over which the normalized scalar variance is constant. The relatively large amount of available wall turbulence data either provides reasonably good support for this hypothesis or at least exhibits a trend that is consistent with the predictions of this hypothesis. The relationship between the proposed scaling and the traditional wall scaling is discussed. Possible ultimate statistical states of wall turbulence are also proposed.