Bifurcations in a quasi-two-dimensional Kolmogorov-like flow
Bifurcations in a quasi-two-dimensional Kolmogorov-like flow
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DOI：
10.1017/jfm.2017.553
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发表时间：
2017-10-10
影响因子：
3.7
通讯作者：
Schatz, Michael F.
中科院分区：
文献类型：
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作者：
Tithof, Jeffrey;Suri, Balachandra;Schatz, Michael F.
我们提出了一个相结合的实验和理论研究的主要和次要的不稳定性在Kolmogorov流。该实验使用具有近似正弦空间轮廓的电磁强迫来驱动悬浮在介电流体的薄润滑层上的电解质薄层中的准二维（Q2 D）剪切流。理论分析基于二维（2D）模型（Suri等人，Phys. Fluids，第26（5）卷，2014，053601），通过对全三维Navier-Stokes方程进行深度平均从第一原理导出。随着强迫强度的增加，实验中的Q2 D流动经历了一系列的分叉，这与直接数值模拟的2D模型的结果进行了比较。的约束和强迫配置文件的影响进行了研究，假设空间周期性和严格的正弦强迫，以及模拟与现实的无滑移边界条件和实验验证的强迫配置文件。我们发现，只有模拟受到物理无滑移边界条件和一个现实的强迫配置文件提供了密切的，定量的协议与实验。我们的分析提供了额外的验证的二维模型，以及正确建模的强迫和边界条件的重要性的示范。
We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a two-dimensional (2D) model (Suri et al., Phys. Fluids, vol. 26 (5), 2014, 053601), derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.