局部诱导近似下涡丝的运动：外生涡丝坐标空间中DaRios-Betchov方程的重新表述
Motion of a Vortex Filament in the Local Induction Approximation: Reformulation of the Da Rios-Betchov Equations in the Extrinsic Filament Coordinate Space
摘要：
在识别的高度非平凡的任务计算的逆Hasimoto变换映射的内在几何参数空间到外在涡丝坐标空间的Da Rios-Betchov方程在后者的空间中的一个重新制定。本文给出的非线性局部涡丝结构解在小振幅极限下与Betchov-Hasimoto解的细节一致，并且与旋转流体中螺旋扭转孤立波在集中涡上传播的实验观测定性一致。本公式还提供了涡丝的滑动运动对涡演化的可辨别的影响。
英文摘要：
In recognition of the highly non-trivial task of computation of the inverse Hasimoto transformation mapping the intrinsic geometric parameter space onto the extrinsic vortex filament coordinate space a reformulation of the Da Rios-Betchov equations in the latter space is given. The nonlinear localized vortex filament structure solution given by the present formulation is in detailed agreement with the Betchov-Hasimoto solution in the small-amplitude limit and is also in qualitative agreement with laboratory experiment observations of helical-twist solitary waves propagating on concentrated vortices in rotating fluids. The present formulation also provides for a discernible effect of the slipping motion of a vortex filament on the vortex evolution.
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