Abstract—This work considers the linear and nonlinear stability of a two-layer Couette flow in a horizontal channel. At the first stage, the Navier–Stokes equations are linearized in both phases. We then solve the spectral problem and investigate the dynamics of periodic disturbances in a wide range of changes in the volumetric content of liquids and the velocity of the top plate. Both the neutral and the fastest growing disturbances of the unstable interface mode are calculated. At the second stage, nonlinear stationary traveling wave regimes were calculated for the Couette flow in a horizontal channel using the complete Navier–Stokes equations for both liquids. The results are compared to the experimental data available in the literature.

摘要—这项工作考虑了水平通道中两层Couette流的线性和非线性稳定性。在第一阶段，Navier-Stokes方程在两个阶段都线性化。然后，我们解决了光谱问题，并研究了在液体体积含量和顶板速度变化的大范围内周期性扰动的动力学。同时计算了不稳定界面模式的中性和增长最快的干扰。在第二阶段，使用两种液体的完整Navier–Stokes方程计算水平通道中Couette流的非线性平稳行波规律。将结果与文献中提供的实验数据进行比较。