Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Flow transition from laminar to turbulent mode (and vice versa)-that is, the initiation of turbulence-is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/ or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence gamma (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where gamma = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y(+) = 1, where y(+) is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of gamma against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, gamma approximate to 25, and for plate flow, gamma approximate to 151.5. These findings suggest that a certain combination of gamma and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence. (C) 2019 THE AUTHOR. Published by Elsevier LTD on behalf of Chinese Academy of Engineering and Higher Education Press Limited Company. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).