Orbits of a system of three point vortices and the associated chaotic mixing.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0232416
David G Dritschel, Gregory N Dritschel, Richard K Scott
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引用次数: 0

Abstract

We study the general periodic motion of a set of three point vortices in the plane, as well as the potentially chaotic motion of one or more tracer particles. While the motion of three vortices is simple in that it can only be periodic, the actual orbits can be surprisingly complex and varied. This rich behavior arises from the existence of both co-linear and equilateral relative equilibria (steady motion in a rotating frame of reference). Here, we start from a general (unsteady) co-linear array with arbitrary vortex circulations. The subsequent motion may take the vortices close to a distinct co-linear relative equilibrium or to an equilateral one. Both equilibrium states are necessarily unstable, as we demonstrate by a linear stability analysis. We go on to study mixing by examining Poincaré sections and finite-time Lyapunov exponents. Both indicate widespread chaotic motion in general, implying that the motion of three vortices efficiently mixes the nearby surrounding fluid outside of small regions surrounding each vortex.

三点旋涡系统的轨道及相关的混沌混合。
我们研究了平面上一组三点涡旋的一般周期运动,以及一个或多个示踪粒子的潜在混沌运动。虽然三个漩涡的运动很简单,只能是周期性的,但实际的轨道却出奇地复杂多变。这种丰富的行为源于共线性和等边相对平衡(旋转参照系中的稳定运动)的存在。在这里,我们从一个具有任意涡旋环流的一般(非稳态)共线性阵列开始。随后的运动可能会使涡旋接近明显的共线相对平衡或等边相对平衡。正如我们通过线性稳定性分析所证明的,这两种平衡状态都必然是不稳定的。我们接着通过研究波恩卡莱截面和有限时间李亚普诺夫指数来研究混合问题。二者都表明一般情况下存在广泛的混沌运动,这意味着三个漩涡的运动有效地混合了每个漩涡周围小区域以外的附近流体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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