Bulk flow scaling for turbulent channel and pipe flows

Abstract

We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel versus circular pipe) by a variational calculation for a large-scale energy length, which characterizes its bulk flow scaling by a simple exponent, i.e. $m=4$ for channel and 5 for pipe. The predicted mean velocity shows excellent agreement with several dozen sets of quality empirical data for a wide range of the Reynolds number (Re), with a universal bulk flow constant $\kappa \approx 0.45$. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.

4 pages, 4 figures

References in corpus (2)

• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Analytic prediction for planar turbulent boundary layers

Cited by in corpus (1)

• Similarity model for corner roll in turbulent Rayleigh-Benard convection