The motion of a vortex on a closed surface of constant negative curvature

Full text
Author(s):	Grotta Ragazzo, C. Total Authors: 1
Document type:	Journal article
Source:	PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SC; v. 473, n. 2206 OCT 1 2017.
Web of Science Citations:	2
Abstract
The purpose of this work is to present an algorithm to determine the motion of a single hydrodynamic vortex on a closed surface of constant curvature and of genus greater than one. The algorithm is based on a relation between the Laplace-Beltrami Green function and the heat kernel. The algorithm is used to compute the motion of a vortex on the Bolza surface. This is the first determination of the orbits of a vortex on a closed surface of genus greater than one. The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface. Some of these equilibria allow for the construction of the first two examples of infinite vortex crystals on the hyperbolic disc. The following theorem is proved: `a Weierstrass point of a hyperellitic surface of constant curvature is always a vortex equilibrium'. (AU)

FAPESP's process:	16/25053-8 - Dynamics and geometry in low dimensions
Grantee:	André Salles de Carvalho
Support Opportunities:	Research Projects - Thematic Grants