On the neutral curve of the flat-plate boundary layer: comparison between experiment, Orr–Sommerfeld theory and asymptotic theory
On the neutral curve of the flat-plate boundary layer: comparison between experiment, Orr–Sommerfeld theory and asymptotic theory
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平板边界层中性曲线：实验、奥尔-索末菲理论与渐近理论的比较
DOI：
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发表时间：
1995
影响因子：
3.7
通讯作者：
J. Healey
中科院分区：
文献类型：
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作者：
J. Healey
使用奥尔-索末菲方程计算了平板边界层的中性稳定性曲线，并与使用上分支和下分支尺度获得的曲线进行了比较。奥尔-索末菲结果与实验相关雷诺数下的下分支标度非常吻合，但仅当 Rδ > 105 时才与上分支标度吻合。结果表明，当 Rδ > 105 时，临界层仅从粘性壁层中出现。这表明，对于 Rδ < 105，当临界层位于粘性壁层内时，扰动具有三层结构，即使对于中性层的上分支也是如此。曲线（如果保留跨越关键层的相位跳变，则可以达到该曲线）。随着上分支雷诺数的增加，从三层结构到五层结构的转变发生得相对突然，并且可以与 Tietjens 函数中的平方根分支点相关联。本质上，下分支和上分支缩放属于两种不同的模式，第一种具有三层结构，第二种具有五层结构。模态在分支点处连接，并且每个模态的中性曲线连接以给出靠近该分支点的单个曲线。上分支中性曲线和下分支中性曲线的渐近展开式取决于色散关系的解析性，因此分支点的接近程度表明这些展开式容易出现不准确的情况。这解释了五层分析对发生转变的雷诺数做出的不良中性曲线预测。
The neutral stability curve for the flat-plate boundary layer has been calculated using the Orr–Sommerfeld equation and compared to those obtained using upper- and lower-branch scalings. The Orr–Sommerfeld results agree well with the lower-branch scaling at Reynolds numbers relevant to experiment, but agree well with the upper-branch scaling only for Rδ > 105. It is shown that the critical layer only emerges from the viscous wall layer when Rδ > 105. This suggests that for Rδ < 105, when the critical layer lies within the viscous wall layer, the disturbance has a triple-deck structure, even for the upper branch of the neutral curve (which can be reached if the phase jump across the critical layer is retained). The transition from a triple-deck to a five-deck structure with increasing Reynolds number on the upper branch occurs relatively abruptly and can be associated with a square-root branch point in the Tietjens function. Essentially, the lower- and upper-branch scalings pertain to two different modes, the first possessing a triple-deck structure, the second a five-deck structure. The modes are connected at the branch point, and the neutral curves of each mode join to give a single curve close to this branch point. The asymptotic expansions for the upper- and lower-branch neutral curves depend upon the analyticity of the dispersion relationship, and so the proximity of the branch point indicates where these expansions will be liable to inaccuracies. This explains the poor neutral-curve predictions made by five-deck analyses at the Reynolds numbers where transition occurs.