Hydrodynamic Vortex on Surfaces
| Autor: | Clodoaldo Grotta Ragazzo, Humberto Henrique de Barros Viglioni |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Surface (mathematics)
MATEMÁTICA APLICADA Applied Mathematics Riemann surface Mathematical analysis General Engineering Equations of motion Weak formulation 01 natural sciences 010305 fluids & plasmas Vortex symbols.namesake Classical mechanics Condensed Matter::Superconductivity Modeling and Simulation Vortex stretching 0103 physical sciences symbols Euler's formula Burgers vortex 010306 general physics Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1432-1467 0938-8974 |
| Popis: | 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 \(\mathbb {R}^3\) are presented. |
| Databáze: | OpenAIRE |
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