A note on the stability of slip channel flows

E. Lauga (1, 2) , Carlo Cossu (3)

1 Division of Engineering and Applied Sciences, Harvard University
2 MIT - Massachusetts Institute of Technology
3 LadHyX - Laboratoire d'hydrodynamique

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. © 2005 American Institute of Physics.

Domains: Physics [physics]; Mechanics [physics]; Fluid mechanics [physics.class-ph]; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Fluids mechanics [physics.class-ph]

E. Lauga, Carlo Cossu. A note on the stability of slip channel flows. Physics of Fluids, 2005, 17 (8), pp.088106. ⟨10.1063/1.2032267⟩. ⟨hal-01023375⟩