The velocity field induced by a helical vortex tube
The velocity field induced by a helical vortex tube
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DOI：
10.1063/1.2061427
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发表时间：
2005-10
影响因子：
4.6
通讯作者：
Y. Fukumoto;V. Okulov
中科院分区：
文献类型：
--
作者：
Y. Fukumoto;V. Okulov
讨论了有限核心厚度对涡流管周围速度场的影响。毕奥-萨伐尔定律的渐近展开以一个小参数（芯半径与曲率半径之比）进行高阶展开，该参数由排列在管中心线上的单极子和偶极子线引起的速度场组成。前者与无限薄的核心相关，并且仅以循环为特征。核心涡度的分布反映了偶极子的强度。该结果应用于螺旋涡流管，偶极子螺旋细丝引起的诱导速度以 Kapteyn 级数的形式获得，这增强了 Hardin 的 [Phys. Fluids 25, 1949 (1982)]单极子的解决方案。使用奇点分离技术，系列的大部分以单极子和偶极子的闭合形式表示。数值计算发现，螺旋螺距越小，相对影响越大...
The influence of finite-core thickness on the velocity field around a vortex tube is addressed. An asymptotic expansion of the Biot-Savart law is made to a higher order in a small parameter, the ratio of core radius to curvature radius, which consists of the velocity field due to lines of monopoles and dipoles arranged on the centerline of the tube. The former is associated with an infinitely thin core and is featured by the circulation alone. The distribution of vorticity in the core reflects on the strength of dipole. This result is applied to a helical vortex tube, and the induced velocity due to a helical filament of the dipoles is obtained in the form of the Kapteyn series, which augments Hardin’s [Phys. Fluids 25, 1949 (1982)] solution for the monopoles. Using a singularity-separation technique, a substantial part of the series is represented in a closed form for both the mono- and the dipoles. It is found from numerical calculation that the smaller the helix pitch is, the larger the relative influe...