Equilibrium turbulent boundary layers

TLDR

The study builds on empirical data from constant‑pressure flows to solve the equations of motion for flows with a constant pressure‑gradient parameter β, and also examines the viscous sublayer and compares eddy‑viscosity hypotheses in a companion paper. The authors extend Clauser and Townsend’s work by hypothesizing a specific form for the effective eddy viscosity. The hypothesized eddy‑viscosity model accurately predicts Clauser’s defect profiles and Stratford’s near‑separating profile, and yields a continuous, analytically precise family of defect profiles covering −0.5 ≤ β ≤ ∞ that span the entire profile except the viscous sublayer.

Abstract

Empirical information is extracted from constant-pressure flows and, on this basis alone, the equations of motion are solved for flows where the pressure gradient parameter, β = δ*( dp / dx )/τ 0 is held constant. The experimental defect profiles of Clauser and the near-separating profile of Stratford are predicted quite well. The present work is an extension of the work of Clauser and Townsend in that a particular form for an effective or eddy viscosity is hypothesized. Here, however, a continuous, and analytically precise family of defect profiles are calculated for the entire range, −0·5 ≤ β ≤ ∞. The solutions span the whole profile with the exception of the viscous sublayer. A detailed consideration of the viscous sublayer and a comparative examination of various eddy viscosity hypotheses are included in a companion paper.