The reconnection of two interacting vortex tubes is a fundamental process in fluid mechanics, which, at very high Reynolds numbers, is associated with the formation of intense velocity gradients. Reconnection is usually studied using two antiparallel tubes which are destabilized via the long-wavelength Crow instability, leading to a very symmetric configuration and to a strong flattening of the cores into thin sheets. Here, we consider the interaction of two initially straight tubes at an angle of $\beta$ and show that by relaxing some symmetries of the problem, a rich phenomenology appears. When the angle between the two tubes is close to $\beta ={90}^{\circ }$, their interaction leads to pairing of small portions of antiparallel tubes, followed by the formation of thin and localized vortex sheets as a precursor of reconnection. The subsequent breakdown of these sheets involves a twisting of the paired sheets, followed by the appearance of a localized cloud of small-scale vortex structures. By decreasing $\beta$, we show that reconnection involves increasingly larger portions of tubes, whose cores are subsequently destabilizing, leaving behind more small-scale vortices. At the smallest values of the angle $\beta$ studied, the two vortices break down through a mechanism, which leads to a cascadelike process of energy conveyance across length scales similar to what was found for previous studies of antiparallel vortex tubes ($\beta =0$) which imposed no symmetries. While, in all cases, the interaction of two vortices depends on the initial condition, the rapid formation of fine-scale vortex structures appears to be a robust feature, possibly universal at very high Reynolds numbers.

中文翻译：

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相互作用涡丝中的级联和重新连接

两个相互作用的涡流管的重新连接是流体力学中的一个基本过程，在非常高的雷诺数下，这与强烈速度梯度的形成有关。通常使用两个反平行的管来研究重新连接，这两个管由于长波长的 Crow 不稳定性而不稳定，导致非常对称的配置和核心的强烈扁平化成薄片。在这里，我们考虑两个初始直管的相互作用$\beta$并表明通过放松问题的一些对称性，出现了丰富的现象学。当两管夹角接近$\beta ={90}^{\circ }$，它们的相互作用导致反平行管的小部分配对，随后形成薄而局部的涡旋片作为重新连接的前兆。这些薄片随后的分解涉及成对薄片的扭曲，随后出现小规模涡旋结构的局部云。通过减少$\beta$，我们表明重新连接涉及越来越大的管子部分，其核心随后不稳定，留下更多的小规模漩涡。在角度的最小值处$\beta$ 研究表明，这两个涡流通过一种机制分解，导致跨长度尺度的级联能量传递过程，类似于先前对反平行涡流管的研究发现的结果。$\beta =0$) 没有施加对称性。虽然在所有情况下，两个涡旋的相互作用取决于初始条件，但精细尺度涡旋结构的快速形成似乎是一个强大的特征，在非常高的雷诺数下可能是普遍的。