On the self-induced motion of a helical vortex
On the self-induced motion of a helical vortex
复制标题
螺旋涡旋的自激运动
DOI：
10.1017/s002211209900422x
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发表时间：
1999
影响因子：
3.7
通讯作者：
D. Wood
中科院分区：
文献类型：
--
作者：
J. Boersma;D. Wood
弯曲涡流附近的速度场包括涡流周围的环流、由涡流曲率引起的分量和由涡流较远部分引起的“剩余部分”。前两个分量是比较好理解的，但其余的只知道几个特定的涡流几何形状，最值得注意的是，涡环。在本文中，我们推导出一个封闭的形式的其余部分是有效的所有值的螺距的一个无限螺旋涡。余项首先从哈丁（1982）螺旋线涡（厚度为零）诱导流动的解中得到。然后，我们用Ricca（1994）对摩尔和Saffman（1972）公式的实现，得到了具有有限圆形涡核的螺旋涡的余项，涡核上的环量是均匀分布的。分析表明，这两个不同的1/4的间距值。这推广了Kuibin和Okulov（1998）的结果，他们得到了小螺距和大螺距下的渐近导数和它们的差。使用Mellin变换对新的封闭形式的分解器进行的渐近分析提供了一个完整的表示，并揭示了对Kuibin & Okulov（1998）的渐近表达式的微小修正。
The velocity field in the immediate vicinity of a curved vortex comprises a circulation around the vortex, a component due to the vortex curvature, and a ‘remainder’ due to the more distant parts of the vortex. The first two components are relatively well understood but the remainder is known only for a few specific vortex geometries, most notably, the vortex ring. In this paper we derive a closed form for the remainder that is valid for all values of the pitch of an infinite helical vortex. The remainder is obtained firstly from Hardin's (1982) solution for the flow induced by a helical line vortex (of zero thickness). We then use Ricca's (1994) implementation of the Moore & Saffman (1972) formulation to obtain the remainder for a helical vortex with a finite circular core over which the circulation is distributed uniformly. It is shown analytically that the two remainders differ by 1/4 for all values of the pitch. This generalizes the results of Kuibin & Okulov (1998) who obtained the remainders and their difference asymptotically for small and large pitch. An asymptotic analysis of the new closed-form remainders using Mellin transforms provides a complete representation by a residue series and reveals a minor correction to the asymptotic expression of Kuibin & Okulov (1998) for the remainder at small pitch.