Vortex breakdown phenomena in the axial vortices is an important feature which occurs frequently in geophysical flows (tornadoes and hurricanes) and in engineering flows (flow past delta wings, Von-Kerman vortex dynamo). We analyze helicity for axisymmetric vortex breakdown and propose a simplified formulation. For such cases, negative helicity is shown to conform to the vortex breakdown. A model problem has been analyzed to verify the results. The topology of the vortex breakdown is governed entirely by helicity density in the vertical plane. Our proposed methodology may be regarded as the prototype for identifying and characterize the breakdowns/eye in more complicated large-scale flows such as tornadoes/hurricanes.

中文翻译：

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Vogel-Escudier 流中涡流击穿气泡与平面螺旋度的相关性

轴向涡流中的涡流击穿现象是地球物理流（龙卷风和飓风）和工程流（流经三角翼，冯克曼涡旋发电机）中经常发生的一个重要特征。我们分析了轴对称涡流击穿的螺旋度，并提出了一个简化的公式。对于这种情况，显示负螺旋度符合涡流击穿。分析了一个模型问题以验证结果。涡流击穿的拓扑结构完全由垂直平面中的螺旋密度控制。我们提出的方法可以被视为识别和表征更复杂的大规模流动（如龙卷风/飓风）中的故障/眼睛的原型。