强迫瑞利-泰勒不稳定性
Centrifugally forced Rayleigh-Taylor Instability
摘要：
旋转对经典引力驱动的瑞利-泰勒不稳定性的影响已经被证明会影响在不稳定界面处发展的扰动的尺度，从而改变波前的传播速度。本文作者认为，这是重力的不稳定效应和旋转的稳定效应之间竞争的结果。在本文中，我们考虑的极端极限的高转速，其中旋转力占主导地位，引力可以忽略不计。两个液体层最初形成同心圆柱体，以旋转轴为中心。该配置可以被认为是流体-流体离心机。有两种类型的扰动的接口，可以被认为是一个方位角扰动周围的圆周的接口和一个静脉曲张的扰动在轴向方向上沿着接口的长度。这是我们在这里考虑的第一种扰动类型，因此流动基本上可以认为是二维的，发生在一个圆形区域内。我们进行了线性稳定性分析的扰动的流体静力学背景状态，并推导出一个四阶Orr-Sommerfeld方程，管理系统。我们考虑系统的稳定和不稳定的配置，无粘和粘性流体，不混溶流体层与表面张力，和混溶流体层，可能有一些初始的密度扩散的动力学。理论预测进行了比较，数值实验和协议被证明是好的。我们不限制我们的分析等体积的流体层，所以我们的结果也有快速旋转系统和机械中的涂层和润滑问题的应用。
英文摘要：
The effect of rotation on the classical gravity-driven Rayleigh-Taylor instability has been shown to influence the scale of the perturbations that develop at the unstable interface and consequently alter the speed of propagation of the front. The present authors argued that this is as a result of a competition between the destabilizing effect of gravity and the stabilizing effect of the rotation. In the present paper we consider the extreme limit of high rotation rates in which rotational forces dominate and gravitational forces may be ignored. The two liquid layers initially form concentric cylinders, centred on the axis of rotation. The configuration may be thought of as a fluid-fluid centrifuge. There are two types of perturbation to the interface that may be considered, an azimuthal perturbation around the circumference of the interface and a varicose perturbation in the axial direction along the length of the interface. It is the first of these types of perturbation that we consider here, and so the flow may be considered essentially two-dimensional, taking place in a circular domain. We carry out a linear stability analysis on a perturbation to the hydrostatic background state and derive a fourth order Orr-Sommerfeld-like equation that governs the system. We consider the dynamics of systems of stable and unstable configurations, inviscid and viscous fluids, immiscible fluid layers with surface tension, and miscible fluid layers that may have some initial diffusion of density. Theoretical predictions are compared with numerical experiments and the agreement is shown to be good. We do not restrict our analysis to equal volume fluid layers and so our results also have applications in coating and lubrication problems in rapidly rotating systems and machinery.
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