圆柱几何中稳定的椭圆涡
Stable Elliptical Vortices in a Cylindrical Geometry
摘要：
我们表明，在一个二维（2D）理想流体（也适用于准2D非中性等离子体柱在轴向磁场），在有限的磁盘大椭圆涡是稳定的。通过比较椭圆态和对称态的能量来满足一个充分条件，无需动力学特征分析。得到了能量的解析小椭圆展开式和有限椭圆的精确数值。膨胀表明稳定的线性l=2 diocotron模式的大涡旋（或等离子体柱）。对二维欧拉方程进行了数值模拟。它们不仅证实了这一充分条件，而且还表明，稳定性持续到较小的涡尺寸。本文还讨论了Briggs，Daughterson和Levy [Phys.Fluids 13，421（1970）]用本征分析法得到衰减的l=2模的原因。
英文摘要：
We show that, in a two-dimensional (2d) ideal fluid (also applies to a column of quasi-2d non-neutral plasma in an axial magnetic field), large elliptical vortices in a finite disk are stable. The stability is established by comparison between energy of elliptical and symmetrical states to satisfy a sufficient condition, without dynamical eigen-analysis. Analytical small ellipticity expansion of energy and exact numerical values for finite ellipticity are both obtained. The expansion indicates stable linear l=2 diocotron modes for large vortices (or plasma columns). Numerical simulations of the 2d Euler equation are also performed. They 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 eigen-analysis is also discussed.
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