Linear stability analysis and direct numerical simulation of two layer channel flow

We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand. The two fluids have the same density but different viscosities. The fluids, when miscible, are separated from each other by a mixed layer of small but finite thickness, across which viscosity changes from that of one fluid to that of the other. When immiscible, the interface is sharp. Our study spans a range of Schmidt numbers, viscosity ratios and location and thickness of the mixed layer. Our two-dimensional linear stability results predict well the behaviour displayed by our three-dimensional direct numerical simulations at early times. In both linear and non-linear regimes, the miscible flow is more unstable than the corresponding immiscible one, and the miscible flow breaks spanwise symmetry more readily to go into three-dimensionality. We show that the miscible flow over our range of parameters is always significantly more unstable than the corresponding immiscible case.