An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc
An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc
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旋转盘上边界层不稳定稳态模式的渐近研究
DOI：
10.1098/rspa.1986.0066
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
P. Hall
中科院分区：
文献类型：
--
作者：
P. Hall
本文研究了旋转圆盘边界层中的高雷诺数定常不稳定性。调查表明，除了Gregory发现的无粘模式外，Stuart&Walker(Phil.翻译过来的。R.Soc.朗德。A248,155(1955))在高雷诺数时，存在一个稳定的短波长模。这种模式的结构由粘性和科里奥利力之间的平衡所固定，不能用无粘性理论来描述。给出了该模式的波数和方向的渐近结构，并对无粘模式进行了类似的分析。扩展过程提供了以自洽的方式考虑非平行影响的能力。Gregory等人的无粘性溶液。进行了修改以考虑到粘性效应。所使用的展开过程同样能够考虑非平行效应。所获得的结果表明了为什么Gregory等人的无粘性方法。应该给出一个很好的近似实验测量的涡旋方向。这些结果也部分解释了为什么无粘性分析不能给出如此好的涡波波数近似值。这两种模式的渐近分析为相应的非线性问题提供了一个起点。
The paper investigates high-Reynolds-number stationary instabilities in the boundary layer on a rotating disc. The investigation demonstrates that, in addition to the inviscid mode found by Gregory, Stuart & Walker (Phil. Trans. R. Soc. Lond. A 248, 155 (1955)) at high Reynolds numbers, there is a stationary short-wavelength mode. This mode has its structure fixed by a balance between viscous and Coriolis forces and cannot be described by an inviscid theory. The asymptotic structure of the wave-number and orientation of this mode is obtained, and a similar analysis is given for the inviscid mode. The expansion procedure provides the capacity of taking non-parallel effects into account in a self-consistent manner. The inviscid solution of Gregory et al. is modified to take account of viscous effects. The expansion procedure used is again capable of taking non-parallel effects into account. The results obtained suggest why the inviscid approach of Gregory et al. should give a good approximation to the experimentally measured orientation of the vortices. The results also explain partly why the inviscid analysis should not give such a good approximation to the wavenumber of the vortices. The asymptotic analysis of both modes provides a starting point for the corresponding nonlinear problems.