Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes

TL;DR

This paper introduces a simple analytical model for high-Reynolds-number turbulent flows in channels and pipes, accurately describing velocity and stress profiles with only three parameters, and clarifying longstanding theoretical debates.

Contribution

The authors propose a novel, physically transparent model that captures turbulent flow profiles at finite Reynolds numbers using minimal parameters, bridging different theoretical approaches.

Findings

Accurately describes mean velocity and Reynolds-stress profiles across a wide Re range.

Uses only three Re-independent parameters for the entire flow profile.

Provides insight into the debate between log-law and power-law theories of turbulence.

Abstract

In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-K\`arm\`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.