Stable elliptical vortices in a circular disk

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/39039

Title:	Stable elliptical vortices in a circular disk
Authors:	Chen,PL
Contributors:	物理研究所
Keywords:	NONNEUTRAL PLASMA-COLUMN;STATISTICAL-MECHANICS;STABILITY THEOREM;VORTEX MERGER;2 DIMENSIONS;EQUILIBRIUM;STATES
Date:	1999
Issue Date:	2010-07-08 14:02:57 (UTC+8)
Publisher:	中央大學
Abstract:	We show that large elliptical vortices in a finite disk are stable in a two-dimensional (2D) ideal fluid (this also applies to a column of quasi-2D non-neutral plasma in an axial magnetic field). The stability is established by comparison between the energy of elliptical and symmetrical states to satisfy a sufficient condition, without dynamical eigenanalysis. Analytical Small ellipticity expansion of system energy and exact numerical values for arbitrary ellipticity are both obtained for uniform vortices. An approximating calculation is presented for general smooth vortices. Numerical simulations of the 2D Euler equation are also performed. The simulations not only confirm the sufficient condition, but also show that the stability persists to smaller Vortex sizes. The reason why decaying l=2 modes were obtained by Briggs, Daugherty, and Levy [Phys. Fluids 13, 421 (1970)] using eigenanalysis is also discussed. [S1063-651X(99)08908-4].
Relation:	PHYSICAL REVIEW E
Appears in Collections:	[Graduate Institute of Physics] journal & Dissertation

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