In this paper we investigate the instability properties of Batchelor vortices with a large swirl number and a fixed axial velocity deficit. In particular, it elucidates the effect of the helicity profile on the instability of the vortices as swirling wakes. In a linear stability analysis, a negative helicity profile destabilised a vortex with a large swirl number; the name given to this instability is ‘helicity instability’. Note that helicity instability is qualified for the case of axial flow with wake. In contrast, a conventional Batchelor vortex was stable at swirl numbers above a value of circulation, which is determined by the axial velocity deficit. The instability was related to a parameter $D$ proportional to the square of the inverse azimuthal vorticity thickness. Decreasing this helicity-profile parameter increased the growth property of the vortex. Such unstable features (helicity effects) were also studied in direct numerical simulations of vortices subjected to small random disturbances at Mach numbers 2.5 and 5.0. The instability based on the vorticity thickness originally grew at the outer edge of the vortex, whereas the instability waves in a conventional Batchelor vortex originate inside the vortex core. The simulation results support the results of the linear stability analysis on the helicity profile when the parameter $D$ is small. Because of the helicity instability, the nonlinear developments yielded a large fluctuation field with many small scales and high radial spreading rates. Even at the Mach number of 5.0, negative helicity exerted a much greater destabilisation effect than a zero entropy gradient. Therefore, the investigated novel effect established a reasonably powerful instability in compressible fluids, which is favourable for supersonic mixing.

在本文中，我们研究了具有大旋流数和固定轴向速度缺陷的Batchelor涡的不稳定性。特别地，它阐明了螺旋形轮廓对涡旋尾流时涡旋不稳定性的影响。在线性稳定性分析中，负螺旋线轮廓使涡旋数大的涡旋不稳定。这种不稳定的名称是“螺旋不稳定”。请注意，对于带有尾流的轴向流，螺旋线的不稳定性是合格的。相比之下，常规的Batchelor涡旋在涡旋数高于循环值（由轴向速度缺陷确定）的循环值时稳定。不稳定性与参数 $ D $有关 与反方位涡度厚度的平方成正比。减小该螺旋度轮廓参数可增加涡旋的生长特性。这种不稳定的特征（螺旋效应）也被直接数值模拟的马赫数为2.5和5.0的小随机扰动涡旋所研究。基于涡旋厚度的不稳定性最初在涡旋的外边缘处增长，而常规Batchelor涡旋中的不稳定性波起源于涡旋核心。当参数 $ D $ 时，仿真结果支持对螺旋度轮廓进行线性稳定性分析的结果 是小。由于螺旋线的不稳定性，非线性的发展产生了一个大的起伏场，具有许多小尺度和高径向扩展率。即使在马赫数为5.0时，负螺旋度也比零熵梯度具有更大的去稳定作用。因此，研究的新颖效果在可压缩流体中建立了相当强大的不稳定性，这对于超音速混合是有利的。