两层系统中平面平行振动流的稳定性
Stability of Plane-Parallel Vibrational Flow In a Two-Layer System
摘要：
本文考虑了两种不同密度和粘度的不可压缩流体在空腔中作水平谐振时，其分离界面的稳定性问题。存在一个简单的基本状态，对应于未扰动的接口和平面平行非定常逆流，这种状态的属性进行了检查。一个线性稳定性问题的接口制定和解决a）为无粘和b）为粘性流体。一个变换的发现，减少了无粘近似下的Mathieu方程的线性稳定性问题。参数共振区域的不稳定性与毛细重力波在接口处的强化进行检查，并将结果进行比较，在粘性的情况下，在一个完整的数值调查。
英文摘要：
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved a) for both inviscid and b) for both viscous fluids. A transformation is found which reduces the linear stability problem under inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.
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