The laminar-to-turbulent transition in viscous fluid flow

TL;DR

This paper investigates the transition from laminar to turbulent flow in viscous fluids, predicting the critical Reynolds number for turbulence onset based on shear stress limits and experimental data.

Contribution

It introduces a theoretical method to predict turbulence onset using ultimate shear stress and flow velocity, validated with experimental data for water.

Findings

Critical Reynolds number predictions align with observed data.

Ultimate shear stress can be experimentally determined from plane Couette flow.

Method applicable to various non-turbulent flows with known velocity fields.

Abstract

The onset of turbulence in laminar flow of viscous fluids is shown to be a consequence of the limited capacity of the fluid to withstand shear stress. This fact is exploited to predict the flow velocity at which laminar flow becomes turbulent and to calculate, on a theoretical basis, the corresponding critical value of the Reynolds number. A constitutive property essential to the present analysis is the ultimate shear stress of the fluid. The paper shows how this stress can be determined experimentally from a test in plane Couette flow. For water at 20 {\deg}C, the value of the ultimate shear stress is calculated from the experiments reported in the literature. This value is then is employed to predict the Reynolds number corresponding to the onset of turbulence in Taylor-Couette flow and in pipe flow of circular cross section. The results are realistic and their significance is assessed critically. The procedure can be applied to predict the onset of turbulence in any non-turbulent flow, provided that the velocity field of the flow is known.