Geometric and topological aspects of vortex filament dynamics under LIA
作者： Renzo L. Ricca
DOI: 10.1007/BFB0102404
关键词:
摘要: Geometric and topological aspects associated with integrability of vortex filament motion in the Localized Induction Approximation (LIA) context (which includes a family local dynamical laws) are discussed. We show how to interpret relation Biot-Savart law soliton invariants can be interpreted terms global geometric functionals knotted solutions. Under basic (zeroth-order) LIA, we prove that filaments shape torus knots T p, q (p, co-prime) (q/p)>1 stable, whereas those (q/p)<1 unstable.
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sci-hub.se 参考文章(11)
R. L. Ricca, H. K. Moffatt, The Helicity of a Knotted Vortex Filament Springer Netherlands. pp. 225- 236 ,(1992) , 10.1007/978-94-017-3550-6_11
Shigeo Kida, A vortex filament moving without change of form Journal of Fluid Mechanics. ,vol. 112, pp. 397- 409 ,(1981) , 10.1017/S0022112081000475
Joel Langer, Ron Perline, Poisson geometry of the filament equation Journal of Nonlinear Science. ,vol. 1, pp. 71- 93 ,(1991) , 10.1007/BF01209148
Yasuhide Fukumoto, Takeshi Miyazaki, Three-dimensional distortions of a vortex filament with axial velocity Journal of Fluid Mechanics. ,vol. 222, pp. 369- 416 ,(1991) , 10.1017/S0022112091001143
G. L. Lamb, Solitons on moving space curves Journal of Mathematical Physics. ,vol. 18, pp. 1654- 1661 ,(1977) , 10.1063/1.523453
Renzo L. Ricca, Physical interpretation of certain invariants for vortex filament motion under LIA Physics of Fluids. ,vol. 4, pp. 938- 944 ,(1992) , 10.1063/1.858274
Renzo L. Ricca, Torus knots and polynomial invariants for a class of soliton equations Chaos. ,vol. 3, pp. 83- 91 ,(1993) , 10.1063/1.165968
William Thomson, Mathematical and physical papers ,(1880)
Hidenori Hasimoto, A soliton on a vortex filament Journal of Fluid Mechanics. ,vol. 51, pp. 477- 485 ,(1972) , 10.1017/S0022112072002307