旋流自由面旋转多面体中离心-重力波共振不稳定性的物理机制
On the physical mechanism of centrifugal-gravity wave resonant instability in swirling free surface rotating Polygons
摘要：
本文对快速旋转圆柱形容器内旋转流的波动共振不稳定性进行了显式分析。将线性动力学分解为水平内侧离心波与外侧垂直重力波的相互作用，以了解离心波的动力学。我们展示了离心波和重力波分别引起的远场速度如何影响彼此的传播速率和振幅增长。我们遵循这一点与分析的不稳定性方面的四波相互作用，两个离心和两个重力的，并解释为什么共振不稳定性只能得到一对之间的两个反向传播的波，一个离心和一个重力。此外，一个近共振制度，不产生不稳定性的结果是从一对反向传播的离心波和一个pro-propagating重力之间的相位锁定配置，其中的相互作用影响波的传播速率，但不影响振幅的增长。
英文摘要：
We present an explicit analysis of wave-resonant instability of swirling flows inside fast rotating cylindrical containers. The linear dynamics are decomposed into the interaction between the horizontal inner centrifugal edge waves, the outer vertical gravity waves with the aim of understanding the dynamics of the centrifugal waves. We show how the far field velocity induced respectively by the centrifugal and the gravity waves affect each other's propagation rates and amplitude growth. We follow this with an analysis of the instability in terms of a four wave interaction, two centrifugal and two gravity ones, and explain why the resonant instability can be obtained only between a pair of two counter-propagating waves, one centrifugal and one gravity. Furthermore, a near resonant regime which does not yield instability is shown to result from a phase-locking configuration between a pair of a counter-propagating centrifugal wave and a pro-propagating gravity one, where the interaction affects the waves' propagation rates but not the amplitude growth.
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