Lower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flows
Lower branch equilibria in Couette flow: the emergence of canonical states for arbitrary shear flows
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库埃特流中的下分支平衡：任意剪切流的规范状态的出现
DOI：
10.1017/jfm.2013.254
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发表时间：
2013
影响因子：
3.7
通讯作者：
Blackburn H
中科院分区：
文献类型：
--
作者：
Blackburn H
我们考虑一系列展向波数的层流平面库埃特流的非线性三维涡波相互作用平衡的发展。结果是使用混合方法计算的，该方法捕获所需的渐近结构，同时提供与平衡状态的完整数值计算的直接链接。每个平衡状态由条纹流、滚动流和在条纹上传播的波组成。使用由这些部分构建的初始条件对有限雷诺数进行直接数值模拟，证实该方案生成纳维-斯托克斯方程的平衡解。考虑高展向波数极限中的涡波相互作用方程的形式预测，对于小波长，平衡呈现出限制在流动中心附近的自相似结构。这些状态不受壁的影响，并导致一类与任意剪切流相关的规范状态。这些预测得到了对展向波数增加值的计算结果的分析的支持。对于这些新规范态的波部分，表明每单位波数的质量比动能密度与波数的幂成比例。
We consider the development of nonlinear three-dimensional vortex–wave interaction equilibria of laminar plane Couette flow for a range of spanwise wavenumbers. The results are computed using a hybrid approach that captures the required asymptotic structure while at the same time providing a direct link with full numerical calculations of equilibrium states. Each equilibrium state consists of a streak flow, a roll flow and a wave propagating on the streak. Direct numerical simulations at finite Reynolds numbers using initial conditions constructed from these parts confirm that the scheme generates equilibrium solutions of the Navier–Stokes equations. Consideration of the form of the vortex–wave interaction equations in the high-spanwise-wavenumber limit predicts that for small wavelengths the equilibria take on a self-similar structure confined near the centre of the flow. These states feel no influence from the walls, and lead to a class of canonical states relevant to arbitrary shear flows. These predictions are supported by an analysis of computational results at increasing values of the spanwise wavenumber. For the wave part of these new canonical states, it is shown that the mass-specific kinetic energy density per unit wavenumber scales with the power of the wavenumber.
弯曲河道流中 Tollmien-Schlichting 波与 Taylor-Görtler 涡流的非线性相互作用
DOI：
10.1098/rspa.1988.0060
发表时间：
1987
期刊：
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
影响因子：
--
作者：
P. Hall;F. Smith
通讯作者：
F. Smith
剪切流中的下分支相干态：转变和控制。
影响因子：
8.6
作者：
Jue Wang;J. Gibson;F. Waleffe
通讯作者：
F. Waleffe