A note on the stability of slip channel flows

We consider the influence of slip boundary conditions on the modal and nonmodal stability of pressure-driven channel flows. In accordance with previous results by Gersting [“Hydrodynamic stability of plane porous slip flow,” Phys. Fluids 17, 2126 (1974)] but in contradiction with the recent investig...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 17; no. 8; pp. 088106 - 088106-4
Main Authors Lauga, Eric, Cossu, Carlo
Format Journal Article
LanguageEnglish
Published Melville, NY American Institute of Physics 01.08.2005
Subjects
Engineering Sciences
Exact sciences and technology
Flows in ducts, channels, nozzles, and conduits
Fluid dynamics
Fluid mechanics
Fluids mechanics
Fundamental areas of phenomenology (including applications)
Mechanics
Physics
Slip flow
Pipe flow
Digital simulation
Hydrodynamic instability
Boundary conditions
Viscous fluids
Parallel plate
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Summary:We consider the influence of slip boundary conditions on the modal and nonmodal stability of pressure-driven channel flows. In accordance with previous results by Gersting [“Hydrodynamic stability of plane porous slip flow,” Phys. Fluids 17, 2126 (1974)] but in contradiction with the recent investigation of Chu [“Instability of Navier slip flow of liquids,” C. R. Mec. 332, 895 (2004)], we show that the slip increases significantly the value of the critical Reynolds number for linear instability. The nonmodal stability analysis, however, reveals that slip has a very weak influence on the maximum transient energy growth of perturbations at subcritical Reynolds numbers. Slip boundary conditions are therefore not likely to have a significant effect on the transition to turbulence in channel flows.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.2032267