The formation of an axisymmetric vortex ring by forcing fluid impulsively through a pipe is examined. An idealized model of the circulation, impulse and energy provided by the injected plug is developed, and these quantities are equated to the corresponding properties of the class of rings with finite cores described by Norbury (1973). It is shown that, as the length-to-diameter aspect ratio LID of the plug increases, the size of the core increases in comparison with all the fluid carried along with the ring, until the limiting case of Hill's spherical vortex is reached. For aspect ratios larger than a certain value it is not possible to produce a single ring while conserving circulation, impulse, volume and energy. This implies that the limiting vortex is 'optimal' in the sense that it has maximum impulse, circulation and volume for a given energy input. While this matching calculation makes the physical mechanism clear, the LID ratio that can be achieved in practice is more appropriately taken from the direct experimental measurements of Gharib et al. (1998) who concluded that the limiting value is L/D = 4. This is close to the value found in our calculation. [References: 21]
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机译：研究了通过迫使流体脉冲通过管道形成的轴对称涡流环。建立了由注入的塞子提供的环流，冲量和能量的理想模型，这些量等于由Norbury（1973）描述的有限核环类的相应属性。结果表明，随着塞子的长径比LID的增加，与随环携带的所有流体相比，芯子的尺寸会增加，直到达到希尔氏球形涡旋的极限情况为止。对于大于一定值的长宽比，在保持循环，脉冲，体积和能量的同时不可能产生单个环。这意味着在给定的能量输入下，极限涡流具有最大的脉冲，循环和体积，从这个意义上说，极限涡流是“最优的”。尽管这种匹配计算使物理机制更加清晰，但实际上可以从Gharib等人的直接实验测量中适当地获得可以实现的LID比。 （1998年）得出结论，极限值为L / D =4。这与我们计算中得出的值接近。 [参考：21]
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