Subcritical transition in plane Poiseuille flow as a linear instability process
Subcritical transition in plane Poiseuille flow as a linear instability process
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平面泊肃叶流中的亚临界转变作为线性不稳定过程
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jacob Cohen
中科院分区：
文献类型：
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作者：
F. Roizner;M. Karp;Jacob Cohen
在这项工作中，一个过渡的情况下，其中大部分的阶段进行了分析。该过渡是由线性瞬态增长机制在平面Poietille流受到一个无限小的二次扰动。一种新的分析近似的线性瞬态增长机制，使我们能够进行二次线性稳定性分析的修改后的基流。这里突出显示了两种可能的过渡路线，它们都对应于叠加在线性瞬态增长上的小的二次扰动。第一种情况是由四个衰减的奇正常模式，形成一个反向旋转的涡对，第二种情况是由五个偶数衰减模式，形成一对反向旋转对。近似的线性瞬态增长阶段的最小数量的模式的组合，使我们能够遵循的过渡阶段分析采用多时间尺度方法。特别是，二次不稳定性阶段分析使用线性工具，并通过获得过渡的瞬态增长的解析表达式所规定的条件下发起的直接数值模拟进行验证。观察到非常好的一致性，验证了理论模型。两个过渡路线之间的相似性进行了讨论，并与平面Couette流获得的类似结果的结果进行了比较。
In this work, a transition scenario is demonstrated, in which most of the stages are followed analytically. The transition is initiated by the linear transient growth mechanism in plane Poiseuille flow subjected to an infinitesimally small secondary disturbance. A novel analytical approximation of the linear transient growth mechanism enables us to perform a secondary linear stability analysis of the modified base-flow. Two possible routes to transition are highlighted here, both correspond to a small secondary disturbance superimposed on a linear transient growth. The first scenario is initiated by four decaying odd normal modes which form a counter-rotating vortex pair; the second is initiated by five even decaying modes which form a pair of counter-rotating pairs. The approximation of the linear transient growth stage by a combination of minimal number of modes allows us to follow the transition stages analytically by employing the multiple time scale method. In particular, the secondary instability stage is followed analytically using linear tools, and is verified by obtaining transition in a direct numerical simulation initiated by conditions dictated by the transient growth analytical expressions. Very good agreement is observed, verifying the theoretical model. The similarities between the two transition routes are discussed and the results are compared with similar results obtained for plane Couette flow.