Helicity effects on inviscid instability in Batchelor vortices
Helicity effects on inviscid instability in Batchelor vortices
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DOI：
10.1017/jfm.2020.388
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发表时间：
2020-06
影响因子：
3.7
通讯作者：
T. Hiejima
中科院分区：
文献类型：
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作者：
T. Hiejima
本文研究了具有大旋流数和固定轴向速度亏损的巴切勒涡的不稳定性。特别地，它阐明了螺旋形对旋涡尾迹不稳定性的影响。在线性稳定性分析中，负螺旋形使大旋流数旋涡失稳；这种不稳定性被称为“螺旋不稳定性”。请注意，螺旋度不稳定性适用于带尾迹的轴向流。相比之下，传统的巴切勒涡在超过环流值时是稳定的，这是由轴向速度亏缺决定的。不稳定性与一个参数D有关，D与反方位角涡度厚度的平方成正比。减小螺旋型参数增加了涡的生长特性。这种不稳定特征（螺旋效应）也在马赫数为2.5和5.0时受到小随机扰动的旋涡的直接数值模拟中进行了研究。基于涡度厚度的不稳定波最初产生于涡的外缘，而传统巴彻勒涡的不稳定波起源于涡核内部。仿真结果支持了参数D较小时螺旋型线的线性稳定性分析结果。由于螺旋度的不稳定性，非线性发展产生了一个具有许多小尺度和高径向扩展速率的大波动场。即使在马赫数为5.0时，负螺旋度也比零熵梯度产生更大的不稳定效应。因此，所研究的新效应在可压缩流体中建立了一个相当强大的不稳定性，这有利于超音速混合。
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.