Critical Reynolds Number for a Natural Transition to Turbulence in Pipe Flows

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.