A tent model of vortex reconnection under Biot-Savart evolution
A tent model of vortex reconnection under Biot-Savart evolution
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DOI：
10.1017/jfm.2017.769
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发表时间：
2018-01-10
影响因子：
3.7
通讯作者：
Moffatt, H. K.
中科院分区：
文献类型：
--
作者：
Kimura, Yoshifumi;Moffatt, H. K.
使用帐篷模型对毕奥-萨伐尔演化下的涡旋重联进行几何和数值研究，该帐篷模型由最初以两个倾斜双曲分支形式组成的涡旋细丝组成；涡流在最接近点处是反平行的。结果表明，这些漩涡的尖端相互接近，并在这样做时加速，在帐篷的顶点形成有限时间奇点。涡旋的最小间隔以及最大速度和轴向应变率表现出近自相似的Leray标度，但速度和应变率的指数稍微偏离它们各自的自相似值-1/2和-1；这种偏差与明显的最小曲率的出现有关，导致尖端处出现尖点结构。在重新连接的瞬间之前，每个漩涡的扭动和扭曲始终为零。通过模型验证，研究了应变率张量的特征值和特征向量的结构：表明第二特征值lambda(2)在涡丝周围具有偶极结构。在尖端，观察到 lambda(2) 为正，并且相应的特征向量与细丝相切，这意味着涡流持续拉伸。
Vortex reconnection under Biot-Savart evolution is investigated geometrically and numerically using a tent model consisting of vortex filaments initially in the form of two tilted hyperbolic branches; the vortices are antiparallel at their points of nearest approach. It is shown that the tips of these vortices approach each other, accelerating as they do so to form a finite-time singularity at the apex of the tent. The minimum separation of the vortices and the maximum velocity and axial strain rate exhibit nearly self-similar Leray scaling, but the exponents of the velocity and strain rate deviate slightly from their respective self-similar values of -1/2 and -1; this deviation is associated with the appearance of distinct minima of curvature leading to cusp structures at the tips. The writhe and twist of each vortex are both zero at all times up to the instant of reconnection. By way of validation of the model, the structure of the eigenvalues and eigenvectors of the rate-of-strain tensor is investigated: it is shown that the second eigenvalue lambda(2) has dipole structure around the vortex filaments. At the tips, it is observed that lambda(2) is positive and the corresponding eigenvector is tangent to the filament, implying persistent stretching of the vortex.