Motion of a Curved Vortex Filament: Higher-Order Asymptotics
Motion of a Curved Vortex Filament: Higher-Order Asymptotics
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弯曲涡丝的运动：高阶渐近学
DOI：
10.1007/978-94-015-9638-1_25
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Y. Fukumoto
中科院分区：
文献类型：
--
作者：
Y. Fukumoto
基于欧拉方程，研究了细长涡管在无粘不可压流体中的三维运动。利用匹配渐近展开法，在小参数ε（涡核半径与曲率半径之比）下，导出了涡丝的速度为O（∈3），从而考虑了涡核自致应变引起的椭圆变形的影响。在局部化归纳近似下，这可归结为局部化归纳族中的一个完全可积的发展方程。
Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated based on the Euler equations. Using the method of matched asymptotic expansions in a small parameter∈, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived toO(∈3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. In thelocalized induction approximation, this is reducible to a completely integrable evolution equation among thelocalized induction hierarchy.