Geometric Characterization of Atmospheric Islands Formed by Two Point Vortices

• Type: Article in International Scientific Journal
• Date: 2025

Authors

Marques, G (Author) Other; Sílvio Gama (Author) FCUP

Journal

Title: Axioms

Vol. 387

Final page: 272

Indexing

ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15