Calculation of the linear stability of liquid flow in a flat channel with walls corrugated along the flow

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. The generalized eigenvalue problem is solved numerically. Three types of disturbances are considered: flat periodic (the Floquet parameter is zero), flat doubly periodic (finite values of the Floquet parameter), and spatial. 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 disturbances that increase over time 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 disturbances are usually more dangerous. The exception is the small amplitude of corrugation, at which plane disturbances are more dangerous.