Lagrangian approach to laminar-turbulent interfaces in transitional pipe flow Journal Article

Author(s): Holzner, Markus; Song, Baofang; Avila, Marc; Hof, Björn
Article Title: Lagrangian approach to laminar-turbulent interfaces in transitional pipe flow
Abstract: Transition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar-turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.
Keywords: Pattern formation; Transition to turbulence; instability; Characteristic length; Entrainment velocities; La-grangian approaches; Numerical resolution; Orders of magnitude
Journal Title: Journal of Fluid Mechanics
Volume: 723
ISSN: 1469-7645
Publisher: Cambridge University Press  
Date Published: 2013-05-01
Start Page: 140
End Page: 162
DOI: 10.1017/jfm.2013.127
Open access: no