Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances
Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances
复制标题
DOI：
10.1017/s0022112096000572
复制
发表时间：
1996-06
影响因子：
3.7
通讯作者：
Xuesong Wu;P. Stewart
中科院分区：
文献类型：
--
作者：
Xuesong Wu;P. Stewart
在本文中，我们发现了一种可以促进三维扰动快速增长的新机制。该机制涉及平面模式和倾斜模式或一对倾斜模式之间的相互作用，它们是锁相的，因为它们具有相同的相速度。这允许在公共关键层内发生强大的非线性相互作用。形成分谐波谐振三元组不需要干扰，因此该机制在比分谐波谐振少得多的限制条件下运行（尽管它的威力稍弱）。我们证明了平面模式和倾斜模式之间的二次相互作用驱动了具有差频的异常大的受迫模式，该受迫模式又与平面模式相互作用以贡献主要的非线性效应。如果倾斜模式的幅度足够小，这种相互作用可以导致倾斜模式超指数增长。由于超指数增长，倾斜模式可能很快就会变得足够强大，足以对平面模式产生反馈效应，从而使相互作用最终变得完全耦合。根据是否存在单个或一对倾斜模式，后续阶段的形式略有不同。这两起案件均已接受调查。特别注意对称平面剪切层，例如平面尾流或射流，其正弦模式的次谐波共振不活动。
In this paper, we have identified a new mechanism which can promote rapid growth of three-dimensional disturbances. The mechanism involves the interaction between a planar mode and an oblique mode, or a pair of oblique modes, which are phase-locked in the sense that they have the same phase speed. This allows a powerful nonlinear interaction to take place within the common critical layer(s). The disturbance is not required to form a subharmonic resonant triad, and hence the mechanism operates under much less restrictive conditions than does subharmonic resonance (although it is somewhat less powerful). We show that the quadratic interaction between the planar mode and the oblique modes drives an exceptionally large forced mode with the difference frequency, which in turn interacts with the planar mode to contribute the dominant nonlinear effect. This interaction can cause the oblique modes to grow super-exponentially provided that their magnitude is sufficiently small. As a result of the super-exponential growth, the oblique mode may soon become strong enough to produce a feedback effect on the planar mode, so that the interactions eventually become fully coupled. This subsequent stage takes slightly different forms depending on whether a single or a pair of oblique modes is present. Both cases are investigated. Particular attention is paid to symmetric plane shear layers, e.g. a planar wake or jet, for which subharmonic resonance of sinuous modes is inactive.