Abstract
The stability of two immiscible fluids with different densities and viscosities is examined for channel flow. A multi-domain Chebyshev collocation spectral method is used for solving the coupled Orr-Sommerfeld stability equations for the entire spectrum of eigenvalues and associated eigenfunctions. Numerical solution of the eigenvalue problem is obtained with the QZ eigenvalue solver and is validated with analytical results derived in the long and short wave limits. A parametric study is carried out to investigate the spectral characteristics and eigenfunction structures related to the shear and interfacial modes of instability. The interactions and mode switching between the two instability modes are investigated. Under certain conditions, the two modes are found to become unstable simultaneously. Mode coalescence can occur in either the stable or the unstable part of the spectrum. In general, the eigenfunction of the most dangerous mode is observed to vary sharply in the neighborhood of the interface and the critical points.
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