Calculation of the Linear Stability of Fluid Flow in a Plane Channel with Transversely Corrugated Walls

The linear stability of plane Poiseuille flow in a channel with the corrugated bottom wall is considered using the full Navier-Stokes equations. The wall is corrugated across the flow, and main flow has a single velocity component. The perturbations of the velocity and pressure fields are three-dimensional and have two wavenumbers. The generalized eigenvalue problem is solved numerically. It is found that the critical Reynolds number, above which perturbations grow with time, depends on the dimensionless amplitude and the corrugation period in a complex way. The corrugation amplitude/period ratio separates the dimensionless corrugation amplitude into two regions in which the dependences of the critical Reynolds number on the corrugation parameters are qualitatively different.