Disturbance amplification in boundary layers over thin wall films
Disturbance amplification in boundary layers over thin wall films
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DOI：
10.1063/1.4940221
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发表时间：
2016-02
影响因子：
4.6
通讯作者：
S. Saha;Jacob Page;T. Zaki
中科院分区：
文献类型：
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作者：
S. Saha;Jacob Page;T. Zaki
在单流体边界层中，条纹在亚临界雷诺数下会扩大，并开始向湍流的早期过渡。引入不同粘度的壁膜可以明显地改变基流的稳定性，特别是摄动条纹的瞬态生长。在双流体流动中，利用半模的形式来识别使动能最大化的最优扰动。对膜相对于外部流动的粘度比范围内的最佳生长的检查揭示了三种不同的放大制度，每种制度都与特征函数的特定组合有关。为了阐明潜在的放大机制，提出了一个模型问题：利用特征函数展开求解初值问题，并用于计算特征函数对的演化。通过适当地选择对，初值问题定性地再现了最优扰动的时间演化过程。
In single-fluid boundary layers, streaks can amplify at sub-critical Reynolds numbers and initiate early transition to turbulence. Introducing a wall film of different viscosities can appreciably alter the stability of the base flow and, in particular, the transient growth of the perturbation streaks. The formalism of seminorms is used to identify optimal disturbances which maximize the kinetic energy in the two-fluid flow. An examination of optimal growth over a range of viscosity ratios of the film relative to the outer flow reveals three distinct regimes of amplification, each associated with a particular combination of the eigenfunctions. In order to elucidate the underlying amplification mechanisms, a model problem is formulated: An initial value problem is solved using an eigenfunction expansion and is used to compute the evolution of pairs of eigenfunctions. By appropriately selecting the pair, the initial value problem qualitatively reproduces the temporal evolution of the optimal disturbance, and...