Transient perturbation growth in time-dependent mixing layers
Transient perturbation growth in time-dependent mixing layers
复制标题
随时间变化的混合层中的瞬态扰动增长
DOI：
10.1017/jfm.2012.562
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发表时间：
2013
影响因子：
3.7
通讯作者：
Arratia C
中科院分区：
文献类型：
--
作者：
Arratia C
我们用数值方法研究了均匀时间演化混合层中三维(3D)扰动的瞬时线性增长，以确定在有限的、预定的时间间隔内，哪些扰动的动能增益是最优的。我们用初始平行速度分布的混合层模型本质上是三维的，最合适的描述是通过ORR和提升机制的组合增长的斜波‘OL’扰动，而对于更长的时间，最优扰动是2D的，类似于KH简正模，具有轻微的增益增强。对于时间演变的KH基流，OL扰动在足够短的时间间隔内继续占据主导地位。然而，对于较长的时间间隔，涉及初级KH波的实质性演化，出现了两大类固有的3D线性最优摄动，在低波数时与众所周知的中心椭圆平移不稳定性有关，在较高波数时与辫子中心双曲型不稳定性有关。在利用OL扰动的增益方面，双曲扰动的效率相对较低，因此仅当基流的时间演变或优化区间的开始时间不允许OL扰动有太多机会增长时，双曲扰动才主导较小的波数(最终)以核心为中心的扰动。当OL微扰可以增长时，它们首先在辫子中增长，然后通过与初级KH波强耦合而触发以椭圆为核心的微扰。如果优化时间间隔包括初级波浪核的配对，则由于初级波浪核在配对期间的显著破坏，在配对事件期间二次椭圆扰动被强烈抑制。
We investigate numerically the transient linear growth of three-dimensional (3D) perturbations in a homogeneous time-evolving mixing layer in order to identify which perturbations are optimal in terms of their kinetic energy gain over a finite, predetermined time interval. We model the mixing layer with an initial parallel velocity distribution profile are inherently 3D, and are most appropriately described as oblique wave ‘OL’ perturbations which grow through a combination of the Orr and lift-up mechanisms, while for longer times, the optimal perturbations are 2D and similar to the KH normal mode, with a slight enhancement of gain. For the time-evolving KH base flow, OL perturbations continue to dominate over sufficiently short time intervals. However, for longer time intervals which involve substantial evolution of the primary KH billows, two broad classes of inherently 3D linear optimal perturbation arise, associated at low wavenumbers with the well-known core-centred elliptical translative instability, and at higher wavenumbers with the braid-centred hyperbolic instability. The hyperbolic perturbation is relatively inefficient in exploiting the gain of the OL perturbations, and so only dominates the smaller wavenumber (ultimately) core-centred perturbations when the time evolution of the base flow or the start time of the optimization interval does not allow the OL perturbations much opportunity to grow. When the OL perturbations can grow, they initially grow in the braid, and then trigger an elliptical core-centred perturbation by a strong coupling with the primary KH billow. If the optimization time interval includes pairing of the primary billows, the secondary elliptical perturbations are strongly suppressed during the pairing event, due to the significant disruption of the primary billow cores during pairing.