CALCULATION OF THE LINEAR STABILITY OF LIQUID FLOW IN A FLAT CHANNEL WITH STREAMWISE WAVY WALLS

Abstract

The full Navier–Stokes equations are used to study the linear stability of plane Poiseuille flow in a channel with the lower wall corrugated along the flow, due to which the flow has two velocity components. A generalized eigenvalue problem is solved numerically. Three types of perturbations are considered: plane periodic (zero Floquet parameter), plane doubly periodic (finite values of the Floquet parameter), and spatial perturbations. Neutral curves are analyzed in a wide range of the corrugation parameter and Reynolds number. It is found that the critical Reynolds number above which time-growing perturbations appear depends in a complex way on the dimensionless amplitude and period of corrugation. It is shown that in the case of flow in a channel with corrugated wall, three-dimensional perturbations are usually more dangerous. The exception is the small amplitude of corrugation at which plane perturbations are more dangerous.