Stability characteristics of wavy walled channel flows

The linear temporal stability characteristics of converging–diverging, symmetric wavy walled channel flows are numerically investigated in this paper. The basic flow in the problem is a superposition of plane channel flow and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the frame work of Floquet theory and solved using the spectral collocation method. Two-dimensional stability calculations indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbance wavenumber–Reynolds number $(αs−R)$ plane, for the wavy channel with wavenumber $λ1=0.2$ and the wall amplitude to semi-channel height ratio, $εw,$ up to 0.1. It is also shown that the two-dimensional wavy channel flows can be modulated by a suitable frequency of wall excitation $ωg,$ thereby stabilizing the flow.