Linear growth rates of types I and II convective modes within the rotating-cone boundary layer
Linear growth rates of types I and II convective modes within the rotating-cone boundary layer
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DOI：
10.1088/0169-5983/42/2/025504
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发表时间：
2010-04
影响因子：
1.5
通讯作者：
S. Garrett
中科院分区：
文献类型：
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作者：
S. Garrett
实验结果表明，旋转锥边界层流动的转捩特性与锥顶角有关。特别是，对反向旋转的Görtler型涡观察到的锥与细长的半角和同向旋转的涡观察到的宽锥。加勒特等人（2009年，《流体力学杂志》，622，209-32）假设细长锥体上存在离心不稳定模式，这种模式比在旋转圆盘和宽锥体上占主导地位的I型（横流）和II型（流线曲率）模式更危险。目前正在开展工作，以澄清这种替代模式，但是，一个清晰的理解类型I和II模式的增长率是至关重要的，最终了解占主导地位的模式如何与半角的变化。在本文中，我们证明了第一和第二类模式的最大增长率减少减少的半角，这清除了替代不稳定模式的优势。此外，有人建议，在75%的锥体表面速度的旋涡将被选择在光滑，干净的旋转锥与半角，使I型模式是占主导地位的。有趣的是，小林和荒井在球形边界层内实验观察到了这种旋涡速度。
Experimental observations have shown that the transition characteristics of the boundary-layer flow over rotating cones depends on the cone half-angle. In particular, pairs of counter-rotating Görtler-type vortices are observed over cones with slender half-angles and co-rotating vortices are observed over broad cones. Garrett et al (2009 J. Fluid Mech. 622 209–32) have hypothesized the existence of a centrifugal instability mode over slender cones that is more dangerous than the types I (crossflow) and II (streamline curvature) modes which dominate over rotating disks and broad cones. Work is currently underway to clarify this alternative mode; however, a clear understanding of the growth rates of types I and II modes is crucial to the ultimate understanding of how the dominant mode changes with half-angle. In this paper, we demonstrate that the maximum growth rate for types I and II modes decreases with reduced half-angle, which clears the way for the dominance of the alternative instability mode. Furthermore, it is suggested that vortices travelling at 75% of the cone surface speed will be selected over smooth, clean rotating cones with half-angle such that the type I mode is dominant. Interestingly, this vortex speed has been experimentally observed by Kobayashi and Arai within the rotating-sphere boundary layer.