Velocity, energy, and helicity of vortex knots and unknots
Velocity, energy, and helicity of vortex knots and unknots
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DOI：
10.1103/physreve.82.026309
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发表时间：
2010-08-17
影响因子：
2.4
通讯作者：
Ricca, R. L.
中科院分区：
文献类型：
--
作者：
Maggioni, F.;Alamri, S.;Ricca, R. L.
在本文中，我们确定的速度，能量，并估计扭曲和扭曲螺旋度的贡献涡丝的形状环面结和unknot（作为环形和极向线圈）在一个完美的流体。计算是通过毕奥-萨伐尔定律的数值积分进行的。涡的复杂性由缠绕数w参数化，缠绕数w由子午线缠绕数与纵向缠绕数之比给出。我们发现，当w < 1时，涡节和环形线圈的运动速度和携带的能量都比相同大小和环量的参考涡环快，而当w > 1时，涡节和极向线圈的运动速度和携带的能量都与参考涡环的运动速度和携带的能量大致相同。螺旋度主要由螺旋贡献决定。最后，我们确认的稳定效果的毕奥-萨伐尔定律的所有结和unknots测试，发现在几个直径的距离结构稳定。我们的结果也适用于超流He-4中的量子化涡旋。
In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w given by the ratio of the number of meridian wraps to that of longitudinal wraps. We find that for w < 1 vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for w > 1 knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by writhe contributions. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid He-4.