Calculation of linear and nonlinear stability of two-layer liquid flow in a horizontal plane channel

The linear and nonlinear stability of two-layer Poiseuille flow in a horizontal channel is considered, and the stability of this flow is compared with the stability of the same flow in a vertical channel. In the first step, the Navier–Stokes equations in both phases are linearized, and the dynamics of periodic perturbations is determined by solving the spectral problem in a wide range of the Reynolds number of the liquid and the gas velocity. The neutral and fastest growing perturbations of the unstable mode are calculated. In the second step, nonlinear wave modes of Poiseuille flow in the horizontal channel are calculated using the full Navier–Stokes equations for both fluids.