Bulk flow scaling for turbulent channel and pipe flows

TL;DR

This paper develops a theory for bulk flow scaling in wall-bounded turbulent flows, accurately predicting mean velocity and flow characteristics across different geometries and Reynolds numbers.

Contribution

The paper introduces a variational approach to derive bulk flow scaling laws that account for boundary geometry symmetries, providing universal constants and predictions.

Findings

Mean velocity predictions match empirical data across Reynolds numbers

Universal bulk flow constant approximately 0.45

Provides predictions for dissipation and turbulent transport

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 $\kappa\approx0.45$. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.