When the cross-section is reduced, a vortex displays spiralling and elasticity, bursting when the external velocity drops. How are these properties affected near a free surface? To answer, a visualization experiment in water is considered where an oscillating obstruction is pitched orthogonally to a rolling oscillation expending minimum energy. We show that short aerated vortices in adverse pressure gradient and shear remain stable during stretching, bursting into bubbles when relaxed after maximum stretching. A vertical aerated double helix (DH) root vortex of contra-rotating vortex tubes is produced near a Rossby number of 0.20. The vortex approaches an inclination of $45^{\circ }$ to the vertical, where stretching intensifies the vorticity to the maximum extent. Vortex inclinations up to $45^{\circ }$ are stable and unstable thereafter. Vortex bursting commences only when the inclination crosses $45^{\circ }$ by the slightest amount. When relaxed, oscillations are produced, breaking the vortex into arrays of bubbles, sometimes precisely at $45^{\circ }$ inclination. The bubble diameter, modelled by equating the effects of the centrifugal force (CF) on the vortex core pressure, to surface tension scales with the inverse of the square of the rotational velocity. When a high CF is withdrawn, the bursting DH aerated vortex cone is crushed due to surface tension. A root vortex and a coiled-up trailing edge vortex together form a compact Hill’s vortex when the highest CF is relieved, bursting into bubbles spectacularly scattered in the unstable sector. The DH vortex breakup is the connection point of vortices in proximity. At high CF, the DH has stacks of Taylor air tubes at $45^{\circ }$ to the external flow bursting when relaxed. Kelvin waves abound when bursting.

中文翻译：

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在自由表面附近爆发的涡流

当横截面减小时，涡流显示出螺旋状和弹性，当外部速度下降时会破裂。这些特性在自由表面附近如何受到影响？为了回答这个问题，考虑在水中进行可视化实验，其中振荡障碍物垂直于滚动振荡，消耗最小能量。我们表明，在拉伸过程中，逆压力梯度和剪切力中的短充气涡流保持稳定，在最大拉伸后放松时会爆裂成气泡。对转涡流管的垂直充气双螺旋 (DH) 根涡在罗斯比数为 0.20 附近产生。涡流向垂直方向倾斜 45^{\circ }$，拉伸最大程度地增强了涡流。高达 $45^{\circ }$ 的涡旋倾角在此之后是稳定和不稳定的。只有当倾斜度超过 $45^{\circ }$ 最轻微时，涡流爆发才开始。当放松时，会产生振荡，将涡旋分解成气泡阵列，有时精确到 $45^{\circ }$ 倾角。通过将离心力 (CF) 对涡流核心压力的影响等同起来的气泡直径与表面张力与旋转速度平方的倒数成比例。当撤回高 CF 时，破裂的 DH 曝气涡流锥由于表面张力而被压碎。当最高 CF 被释放时，根涡和盘绕的后缘涡一起形成一个紧凑的希尔涡，爆裂成气泡，在不稳定的扇区中非常分散。DH 涡旋破裂是附近涡旋的连接点。在高CF下，DH 有成堆的泰勒空气管，价格为 45 美元 ^{\circ }$ 到外部气流在放松时爆裂。爆裂时开尔文波比比皆是。