The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the associated eigenproblem. The neutral stability boundary and the corresponding critical wave number are obtained for liquid - liquid and air - water systems. Depending on the problem parameters, the instability sets in owing to short, intermediate, of long wave most unstable perturbations. Patterns of the most unstable disturbances are reported and discussed. It is shown that the instability arises due to shear, or interfacial mechanisms. Effects of the surface tension and of width/height aspect ratio are also studied. The results support the premise that the stability analysis of stratified two-phase flow in the simpler geometry of two-infinite plates can provide a reasonable estimation of the conditions for which this flow pattern can be considered to be linearly stable.

中文翻译：

---

矩形管道中分层两相流的不稳定性

数值研究了矩形管道中分层两相流的线性稳定性。线性稳定性分析考虑了所有可能的无穷小三维扰动，并通过解决相关的特征问题来进行。得到了液-液和气-水系统的中性稳定边界和相应的临界波数。根据问题参数，不稳定是由于短波、中波、长波最不稳定的扰动而产生的。报告和讨论了最不稳定扰动的模式。结果表明，不稳定性是由剪切或界面机制引起的。还研究了表面张力和宽度/高度纵横比的影响。