Stability of two-layered fluid flows in an inclined channel

A linear stability analysis of two-layer fluid flows in an inclined channel geometry has been carried out. The onset of flow transitions and the spatio-temporal characteristics of secondary flows produced by the flow instabilities have been examined. The effects of density and viscosity stratifications and surface tension on flow structures also have been investigated at various values of Froude numbers (channel inclinations). Multi-domain Chebyshev-Tau spectral methods along with MATLAB QZ eigenvalue solver are used to determine the whole spectrum of the eigenvalues and associated eigenfunctions. The neutral stability diagrams and stability boundaries are constructed for various values of flow parameters. The onset of flow transitions and flow structures predicted by linear stability analysis are compared against experimental results and they agree reasonably well. The results presented in the present paper imply that the shear mode of flow transitions is the one likely to be identified in experiments.