论文标题
集体次要不稳定性：三维边界层流的应用
Collective secondary instabilities: an application to three-dimensional boundary-layer flow
论文作者
论文摘要
在某些线性不稳定的流动中，发现二次不稳定性的波长比主要不稳定模式的波长大得多，因此无法通过经典的浮子分析将其恢复。在这项工作中，我们应用了一种新的公式，以捕获辅助不稳定性耦合主要模式的多个长度尺度。该公式基于二维稳定性分析，再加上Schmid等人最初描述的Bloch波形形式。 （2017年），允许考虑由周期性单元的多次重复产生的高维系统，通过求解尺寸较小的本本特征问题。因此，可以检索耦合多个周期单元的集体不稳定性。该方法应用于受固定的横流涡流的扫描边界层流的二级稳定性，并与Floquet Analysis进行了比较。恢复了两个多模式的不稳定性：对于流式波数$α_v$接近零，大约十二个子单元参与了大波长振荡；尽管$α_v= 0.087 $，观察到了交错的模式，是亚谐波不稳定性的特征。
In some linearly unstable flows, secondary instability is found to have a much larger wavelength than that of the primary unstable modes, so that it cannot be recovered with a classical Floquet analysis. In this work, we apply a new formulation for capturing secondary instabilities coupling multiple length scales of the primary mode. This formulation, based on two-dimensional stability analysis coupled with a Bloch waves formalism originally described in Schmid et al. (2017), allows to consider high-dimensional systems resulting from several repetitions of a periodic unit, by solving an eigenproblem of much smaller size. Collective instabilities coupling multiple periodic units can be thus retrieved. The method is applied on the secondary stability of a swept boundary-layer flow subject to stationary cross-flow vortices, and compared with Floquet analysis. Two multi-modal instabilities are recovered: for streamwise wavenumber $α_v$ close to zero, approximately twelve sub-units are involved in large-wavelength oscillations; whereas a staggered pattern, characteristic of subharmonic instabilities, is observed for $α_v = 0.087$.
