Geometric Characterization of Atmospheric Islands Formed by Two Point Vortices

• Tipo: Artigo em Revista Científica Internacional
• Data: 2025

Autores

Marques, G (Autor) Outra; Sílvio Gama (Autor) FCUP

Revista

Título: Axioms

Vol. 387

Página Final: 272

Indexação

ISI Web of Knowledge - 0 Citações

Outras Informações

ID Authenticus: P-018-FD7

DOI: 10.3390/axioms14040272

Abstract (EN): Generically, in a system with more than three point vortices, there exist regions of stability around each vortex, even if the system is chaotic. These regions are usually called stability islands, and they have a morphology that is hard to characterize. In a system of two or three point vortices, these stability islands are better named vortex atmospheres or atmospheric islands, since the whole system is regular. In this work, we present an analytical study to characterize these atmospheres in two point vortex systems for arbitrary values of the circulations Gamma 1 and Gamma 2 in the infinite two-dimensional plane x,y is an element of R2-the simplest scenario-by studying the dynamics of passive particles in these environments. We use the trajectories of passive particles to find the stagnation points of these systems, the special trajectories that partition R2 in different regions and the analytical expressions that define the boundary of the atmospheric islands. In order to characterize the geometry of these atmospheres, we compute their perimeter and area as a function of gamma=Gamma 1 Gamma 1+Gamma 2, if Gamma 1+Gamma 2 not equal 0. The case Gamma 1+Gamma 2=0 is treated separately, as the perimeter and area of the atmospheres do not depend on the circulations. Furthermore, in this latter case, we observe that the atmospheric island has a very similar morphology to an ellipse, only differing from the ellipse that best approximates the atmosphere by a relative error of approximate to 3.76 parts per thousand in area.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 15