Non-linear resonant instability in boundary layers
Non-linear resonant instability in boundary layers
复制标题
DOI：
10.1017/s0022112071002635
复制
发表时间：
1971-11
影响因子：
3.7
通讯作者：
A. Craik
中科院分区：
文献类型：
--
作者：
A. Craik
本文研究了不稳定边界层中Tollmien-Schlichting波的共振三波组。所考虑的三元组包括一个二维波和两个以与流动方向成相等和相反的角度传播的斜波，使得所有三个波在下游方向上具有相同的相速度。对于这样一个共振三元组非常强大的波的相互作用发生，这可能会导致一个连续和快速的能量转移从主剪切流的扰动。看来，斜波可以特别迅速地增长，有人建议，这种优先增长可能是负责不稳定边界层的三维的快速发展。非线性能量传递主要发生在临界层附近，在临界层处，波的下游传播速度等于主流的速度。理论分析最初进行了一般的主要速度分布，然后，为了证明结果的基本特征，精确的相互作用方程推导出一个特定的配置文件组成的一层恒定剪切边界的均匀流动。给出了一般相互作用方程的一些精确解，其中一个解具有在有限时刻波幅无限大的性质。本文还考察了本理论模型与Klebanoff，Tidstrom &萨金特（1962）实验的可能关联性。
An investigation is made of resonant triads of Tollmien-Schlichting waves in an unstable boundary layer. The triads considered are those comprising a two-dimensional wave and two oblique waves propagating at equal and opposite angles to the flow direction and such that all three waves have the same phase velocity in the downstream direction. For such a resonant triad remarkably powerful wave interations take place, which may cause a continuous and rapid transfer of energy from the primary shear flow to the disturbance. It appears that the oblique waves can grow particularly rapidly and it is suggested that such preferential growth may be responsible for the rapid development of three-dimensionality in unstable boundary layers. The non-linear energy transfer primarily takes place in the vicinity of the critical layer where the downstream propagation velocity of the waves equals the velocity of the primary flow. The theoretical analysis is initially carried out for a general primary velocity profile; then, in order to demonstrate the essential features of the results, precise interaction equations are derived for a particular profile consisting of a layer of constant shear bounded by a uniform flow. Some exact solutions of the general interaction equations are presented, one of which has the property that the wave amplitudes become indefinitely large at a finite time. The possible relevance of the present theoretical model to the experiments of Klebanoff, Tidstrom & Sargent (1962) is examined.