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Updated: Jul 16, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Critical Reynolds number for a natural transition to turbulence in pipe flows
1Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel. guyb@uiuc.edu
Abstract:
Experimental results obtained over more than a century have shown that laminar flow in a circular pipe becomes naturally turbulent at a critical Reynolds number of Re approximately 2000. In this Letter a theoretical explanation, based on the minimum energy of an axisymmetric deviation (from the developed pipe flow profile), is suggested for this critical value. It is shown that for Re>1840 the minimum energy of the deviation, associated with the central part of the pipe, becomes a global minimum for triggering secondary instabilities. For Re<1840 the global minimum energy deviation is located next to the pipe wall. Previous experimental observations support this explanation.
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