Computation of the Linear and Nonlinear Stability of a Two-Layer Couette Flow
We consider both linear and nonlinear stability of a two-layer Couette flow in a horizontal channel. As a first step, we linearize the Navier–Stokes equations in both phases and solve the general spectral problem. Varying velocity of the channel upper plate and the ratio of the fluids volumes in a wide range, we define the periodical disturbances behavior in time. We find both the neutral and the fastest growing disturbances of the unstable interface mode. As a second step, we obtain the nonlinear wavy regimes of a two-layer Couette flow in a horizontal channel using the full Navier–Stokes equations in both phases. We carry out comparison with the available experimental data