Stability of Relative Equilibria in the Problem of <i>N</i>+1 Vortices

Cabral, Hildeberto E.; Schmidt, Dieter

doi:10.1137/s0036141098302124

Cited by 56 publications

(66 citation statements)

References 5 publications

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“…Concerning the influence of reasonable perturbations, we confirm instability of QBO east phase and stability of QBO west phase during north hemispheric winter period. This is also consistent with the theoretical stability analysis of Cabral and Schmidt (2000). Thereby, we propose a dynamical explanation of the observed HoltonÁTan effect during winter period by point vortex theory.…”

Section: Discussionsupporting

confidence: 91%

“…By applying the theoretical stability condition of Cabral and Schmidt (2000), we propose a novel idea to explain the stability of the polar vortex and its interaction with the east and west phases of the QBO by n 08'1 point vortex systems with 8 equally spaced vortices on a polygon and '1 polar vortex.…”

Section: Relative Point Vortex Equilibriamentioning

confidence: 99%

“…Already in 1883, Thomson investigated stability studies on multiple, equally spaced point vortices on a circle (Thomson, 1883), followed by many other works in this field, see for example Campbell and Ziff (1978), Cabral and Schmidt (2000), or Aref et al (2012). Charney (1963) extended those configurations of 7, 8 and 16 vortices to atmospheric motion.…”

Section: Application On Planetary Scale: the Stability Of The Polar Vmentioning

confidence: 99%

“…In this case, small perturbations are growing leading to a complete different configuration, while a stable equilibrium will hardly be affected by perturbations. To examine the stability for the N ' 1 relative equilibrium, we consider the criterion of Cabral and Schmidt (2000) for the Lyapunov stability:…”

Section: Application On Planetary Scale: the Stability Of The Polar Vmentioning

confidence: 99%

See 3 more Smart Citations

Applications of point vortex equilibria: blocking events and the stability of the polar vortex

Müller¹,

Névir²,

Schielicke³

et al. 2015

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TThe present study investigates non-linear dynamics of atmospheric flow phenomena on different scales as interactions of vortices. Thereby, we apply the idealised, two-dimensional concept of point vortices considering two important issues in atmospheric dynamics. First, we propose this not widely spread concept in meteorology to explain blocked weather situations using a three-point vortex equilibrium. Here, a steady state is given if the zonal mean flow is identical to the opposed translational velocity of the vortex system. We apply this concept exemplarily to two major blocked events establishing a new pattern recognition technique based on the kinematic vorticity number to determine the circulations and positions of the interacting vortices. By using reanalysis data, we demonstrate that the velocity of the tripole in a westward direction is almost equal to the westerly flow explaining the steady state of blocked events. Second, we introduce a novel idea to transfer a stability analysis of a vortex equilibrium to the stability of the polar vortex concerning its interaction with the quasi-biennial oscillation (QBO). Here, the point vortex system is built as a polygon ring of vortices around a central vortex. On this way we confirm observations that perturbations of the polar vortex during the QBO east phase lead to instability, whereas the polar vortex remains stable in QBO west phases. Thus, by applying point vortex theory to challenging problems in atmospheric dynamics we show an alternative, discrete view of synoptic and planetary scale motion.

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Section: Discussionsupporting

confidence: 91%

Section: Relative Point Vortex Equilibriamentioning

confidence: 99%

Section: Application On Planetary Scale: the Stability Of The Polar Vmentioning

confidence: 99%

Section: Application On Planetary Scale: the Stability Of The Polar Vmentioning

confidence: 99%

See 2 more Smart Citations

Applications of point vortex equilibria: blocking events and the stability of the polar vortex

Müller¹,

Névir²,

Schielicke³

et al. 2015

Tellus A: Dynamic Meteorology and Oceanography

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“…Разделы 3 и 6 посвящены изучению свойств центрально-симметричных движений таких структур в случае, когда вихри нижнего слоя образуют правильный A-угольник, а вихрь верхнего слоя занимает центральное положение. В смысле постановки задачи и исследования кинемати-ческих характеристик стационарных состояний предложенная модель может трактоваться как обобщение на бароклинный случай известных результатов классической динамики вихрей (на-пример, [2,3,10,22,24,39,43,44]). Однако это не относится к проведенному в цитированных работах исследованию устойчивости вихревых структур, которое остается вне рамок нашего ис-следования.…”

Section: Introductionunclassified

Some properties of motion of A+1 vortices in a two-layer rotating fluid

Sokolovskiy¹,

Verron

2006

Nelin. Dinam.

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Получено 7 февраля 2006 г.Исследуются характерные свойства движений A + 1 погруженных в двухслойную жидкость точечных вихрей с A плоскостями симметрии. Предполагается, что центральный вихрь принадлежит верхнему слою, а равносторонняя A-гональная конфигурация вихрей равной интенсивности -нижнему. Приводится анализ теоретически возможных стационарных движений при A 2. Для A = 2 методами качественного анализа осуществлена классификация про-извольных движений вихревых структур, а также получены предварительные результаты по численному исследова-нию устойчивости симметричных конфигураций.Ключевые слова: двухслойная жидкость, точечный вихрь, вихревые структуры, хореогра-фия, фазовый портрет. M. A. Sokolovskiy, J. Verron Some properties of motion of A + 1 vortices in a two-layer rotating fluidThe paper explores the properties of motion of A + 1 point vortices with A planes of symmetry immersed into a twolayer fluid. The central vortex is supposed to be in the upper layer while the other A vortices have equal intensity and form a regular A-gon configuration in the lower layer. For A 2, we study possible stationary motions. For A = 2, using methods of qualitative analysis, we classify the motions of this vortical structure and obtain preliminary numerical results concerned with stability of symmetrical configurations.

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Corotating five point vortices in a plane

Nakaki

2002

Fluid Mechanics and Its Applications

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Stability of Relative Equilibria in the Problem of N+1 Vortices

Cited by 56 publications

References 5 publications

Applications of point vortex equilibria: blocking events and the stability of the polar vortex

Applications of point vortex equilibria: blocking events and the stability of the polar vortex

Some properties of motion of A+1 vortices in a two-layer rotating fluid

Corotating five point vortices in a plane

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