Stability of two-layer flows past slippery surfaces. I. Horizontal channels

We study the role of wall slip on the stability of a two-layered plane Poiseuille flow. The equations of motion for the base flow state are derived, and a linear stability analysis is carried out to arrive at the fourth-order Orr–Sommerfeld equations for the fluid layers. An asymptotic analysis is conducted for wavenumbers in the long wavelength limit. The Orr–Sommerfeld equations are solved numerically using a multidomain Chebyshev Collocation Method to arrive at the spectrum of eigenvalues and their associated eigenfunctions. The effect of wall slip on the stability characteristics of the flow system is examined in greater detail. It is observed that slip brings about a stabilizing, as well as a destabilizing effect on the flow system.