On the inviscid instability of certain two-dimensional vortex-type flows
On the inviscid instability of certain two-dimensional vortex-type flows
复制标题
某些二维涡型流动的无粘不稳定性
DOI：
10.1017/s0022112067001090
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发表时间：
1967
影响因子：
3.7
通讯作者：
A. Timme
中科院分区：
文献类型：
--
作者：
By Alfons Michalke;A. Timme
作为对二维自由边界层中涡流破坏现象的贡献，本文讨论了单个圆柱形（即二维）涡流是否会变得不稳定的问题。因此，当出现在自由边界层中时，单个涡旋可以通过轴对称涡旋模型来近似。然后将旋转流体的无粘稳定性理论应用于该涡流模型。根据一般稳定性准则，发现仅由一种符号的涡量组成的涡旋根据瑞利准则是稳定的，但是，如果涡量在轴外具有极值，则对于圆柱扰动可能会变得不稳定。此外，还对三种特殊类型的涡流进行了稳定性计算。结果发现，它们对于圆柱扰动比对于三维扰动更不稳定。
As a contribution to the breakdown phenomenon of vortices in a two-dimensional free boundary layer, this paper deals with the question whether a single cylindrical (i.e. two-dimensional) vortex can become unstable. For this reason a single vortex, as it occurs in a free boundary layer, is approximated by an axisymmetrical vortex model. The inviscid stability theory of rotating fluids is then applied to this vortex model. By general stability criteria it was found that a vortex consisting of vorticity of one sign only is stable according to the Rayleigh criterion, but, if the vorticity has an extremum value outside the axis, may become unstable with respect to cylindrical disturbances. Furthermore, stability calculations for three special types of vortex were performed. It was found that they were more unstable with respect to cylindrical disturbances than to three-dimensional ones.