Generalized Scaling and Model for Friction in Wall Turbulence

Abstract

We present a novel generalized scaling framework and predictive model for wall friction in turbulent flows. The scaling is derived from the dynamical equations, and total mean-flow kinetic energy and the velocity profile shape factor are used as surrogates for dynamical and boundary condition effects. Veracity of the present approach is assessed using data from the literature spanning unprecedented ranges of flow types, Reynolds numbers, accelerations, and history effects. Unlike previous models that solely apply to standard flows, the present framework reconciles nonstandard flows with standard flows and enables accurate estimates of wall friction in numerical simulations and experiments without resolving the viscous sublayer or using the law of the wall.