Hydrodynamic Vortex on Surfaces

Autor(es)

Ragazzo, Clodoaldo Grotta ^[1] ; de Barros Viglioni, Humberto Henrique ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[2] Univ Fed Sergipe, Ctr Cincias Exatas & Tecnol, Sao Cristovao - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF NONLINEAR SCIENCE; v. 27, n. 5, p. 1609-1640, OCT 2017.
• Citações Web of Science: 3

Resumo

The equations of motion for a system of point vortices on an oriented Riemannian surface of finite topological type are presented. The equations are obtained from a Green's function on the surface. The uniqueness of the Green's function is established under hydrodynamic conditions at the surface's boundaries and ends. The hydrodynamic force on a point vortex is computed using a new weak formulation of Euler's equation adapted to the point vortex context. An analogy between the hydrodynamic force on a massive point vortex and the electromagnetic force on a massive electric charge is presented as well as the equations of motion for massive vortices. Any noncompact Riemann surface admits a unique Riemannian metric such that a single vortex in the surface does not move ({''}Steady Vortex Metric{''}). Some examples of surfaces with steady vortex metric isometrically embedded in R-3 are presented. (AU)

• Processo FAPESP: 11/16265-8 - Dinâmica em baixas dimensões
• Beneficiário: Edson Vargas
• Modalidade de apoio: Auxílio à Pesquisa - Temático