A note on the stability of slip channel flows

Abstract

We consider the influence of slip boundary conditions on the modal and non-modal stability of pressure-driven channel flows. In accordance with previous results by Gersting (1974) (Phys. Fluids, 17) but in contradiction with the recent investigation of Chu (2004) (C.R. Mecanique, 332), we show that slip increases significantly the value of the critical Reynolds number for linear instability. The non-modal stability analysis however reveals that the 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.