Three-dimensional instabilities in steady and unsteady non-parallel boundary layers, including effects of Tollmien-Schlichting disturbances and cross flow
Three-dimensional instabilities in steady and unsteady non-parallel boundary layers, including effects of Tollmien-Schlichting disturbances and cross flow
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稳态和非稳态非平行边界层中的三维不稳定性，包括 Tollmien-Schlichting 扰动和横流的影响
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
F. Smith
中科院分区：
文献类型：
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作者：
P. Stewart;F. Smith
对于存在明显不平行性的稳定和不稳定 2D 或 3D 边界层，考虑三维 (3D) 线性稳定性属性。这种稳定性令人感兴趣的非平行流的两个主要例子是，首先是稳态运动、过粗糙度元素、横流或大规模分离，其次是不稳定的 2D Tollmien-Schlichting (TS) 运动及其相关的二次不稳定性问题。这里介绍了高频稳定性分析。研究发现，对于 2DTS 或稳定边界层，随着非平行流效应的增加，最大 TS 空间增长率的方向存在摆动，从平行流的 0° 到远离自由流方向的 64.68°。这些效应主要取决于边界层位移的局部斜率，并且实际上与边界层位移的局部斜率成正比。横流也会对 TS 不稳定性产生深远的影响。还讨论了对更高幅度和/或更快尺度扰动、其二次不稳定性和非线性相互作用的进一步影响。
Three-dimensional (3D) linear stability properties are considered for steady and unsteady 2D or 3D boundary layers with significant non-parallelism present. Two main examples of such non-parallel flows whose stability is of interest are, firstly, steady motion, over roughness elements, in cross flow, or in large-scale separation and, secondly, unsteady 2D Tollmien-Schlichting (TS) motion, with its associated question of secondary instabilities. A high-frequency stability analysis is presented here. It is found that, for 2DTS or steady boundary layers, there is a swing in the direction of maximum TS spatial growth rate, from 0° for parallel flow towards 64.68° away from the free-stream direction, as the nonparallel flow effects increase. These effects then depend principally on, and indeed are proportional to, the local slope of the boundary-layer displacement. Cross flow can also have a profound impact on TS instabilities. Further implications for higher-amplitude and/or fasterscale disturbances, their secondary instability, and nonlinear interactions, are also discussed.