Absolute instability of the boundary layer on a rotating disk
Absolute instability of the boundary layer on a rotating disk
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DOI：
10.1017/s0022112095003405
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发表时间：
1995-09
影响因子：
3.7
通讯作者：
R. Lingwood
中科院分区：
文献类型：
--
作者：
R. Lingwood
本文研究了在静止流体中旋转的圆盘上的边界层流动的理论行为。在时间t = 0时，流以一定半径被脉冲激发。本文分析了流场的无粘稳定性及含粘性、科里奥利效应和流线曲率效应的稳定性。在这两种情况下，在一定的参数空间范围内，流动是绝对不稳定的，即在空间的每一个不动点扰动随时间增长。在此范围之外，气流对流不稳定或稳定。不稳定性的绝对性质或对流性质是通过检查色散关系的分支点奇点来确定的。雷诺数大于510时存在绝对不稳定性。从层流到湍流过渡开始的实验观测值平均值为513。认为绝对不稳定性可能导致向湍流过渡的开始。无粘分析结果表明，绝对失稳不是由科里奥利效应引起的，也不是由流线曲率效应引起的。这表明这种机制在后掠翼上是可能的，在那里科里奥利效应不存在，但边界层在其他方面是相似的。
This paper is concerned with the theoretical behaviour of the boundary-layer flow over a disk rotating in otherwise still fluid. The flow is excited impulsively at a certain radius at time t = 0. This paper analyses the inviscid stability of the flow and the stability with viscous, Coriolis and streamline curvature effects included. In both cases, within a specific range of the parameter space, it is shown that the flow is absolutely unstable, i.e. disturbances grow in time at every fixed point in space. Outside this range, the flow is convectively unstable or stable. The absolute or convective nature of the instabilities is determined by examining the branch-point singularities of the dispersion relation. Absolute instability is found for Reynolds numbers above 510. Experimentally observed values for the onset of transition from laminar to turbulent flow have an average value of 513. It is suggested that absolute instability may cause the onset of transition to turbulent flow. The results from the inviscid analysis show that the absolute instability is not caused by Coriolis effects nor by streamline curvature effects. This indicates that this mechanism may be possible on swept wings, where Coriolis effects are not present but the boundary layers are otherwise similar.