The stability of a trailing line vortex. Part 2. Viscous theory
The stability of a trailing line vortex. Part 2. Viscous theory
复制标题
尾线涡的稳定性。
DOI：
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发表时间：
1974
影响因子：
3.7
通讯作者：
Frederick Paillet
中科院分区：
文献类型：
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作者：
Frederick Paillet
在之前的一篇论文中，研究了旋转远尾流的非粘性稳定性，并且旋流流在轴对称尾流上的叠加被证明最初是不稳定的，尽管所有研究的模式最终在足够大的旋涡下变得更加稳定。最不稳定的扰动是非轴对称模式，其负方位角波数 n 代表与尾流旋转方向相反的螺旋波路径。扰动增长率似乎随着 |n| 持续增加，而所有具有 |n| 的模式> 1 表示对于非涡流尾流来说完全稳定的扰动。在本分析中，计算了最低的三种负非轴对称模式（n = -1、-2 和 -3）的时间和空间增长率。涡流强度由涡流参数 q 表征，该参数与最大涡流速度与最大轴向速度缺陷之比成正比。与大|n|处的扰动相关的大波数允许 n = −1 模式的最小临界雷诺数为 16 (q ≃ 0·40)。研究的其他两种模式在中性曲线上的最小雷诺数为 31 (n = −2, q = 0·60) 和 57 (n = −3, q = 0·80)。对于每种模式，一旦涡流变得足够大，中性稳定性曲线就会迅速转向无限雷诺数。一些最不稳定的漩涡流被证明具有空间放大系数，几乎是中等雷诺数下非漩涡尾流的最不稳定波数的十倍。
In a previous paper, the inviscid stability of a swirling far wake was investigated, and the superposition of a swirling flow on the axisymmetric wake was shown to be initially destabilizing, although all modes investigated eventually become more stable at sufficiently large swirl. The most unstable disturbances were non-axisymmetric modes with negative azimuthal wavenumber n representing helical wave paths opposite in sense to the wake rotation. The disturbance growth rate appeared to increase continuously with |n|, while all modes with |n| > 1 represented disturbances which are completely stable for the non-swirling wake. In the present analysis, both timewise and spacewise growth rates are calculated for the lowest three negative non-axisymmetric modes (n = −1, −2 and −3). Vortex intensity is characterized by a swirl parameter q proportional to the ratio of the maximum swirling velocity to the maximum axial velocity defect. The large wavenumbers associated with the disturbances at large |n| allow the n = −1 mode to have the minimum critical Reynolds number of 16 (q ≃ 0·40). The other two modes investigated have minimum Reynolds numbers on the neutral curve of 31 (n = −2, q = 0·60) and 57 (n = −3, q = 0·80). For each mode, the neutralstability curve is shown to shift rapidly towards infinite Reynolds numbers once the swirl becomes sufficiently large. Some of the most unstable swirling flows are shown to possess spacewise amplification factors almost ten times that for the most unstable wavenumber for the non-swirling wake at moderate Reynolds numbers.