| Revista: | Revista mexicana de física |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000384012 |
| ISSN: | 0035-001X |
| Autors: | Rendón, Pablo L1 Ley Koo, Eugenio2 |
| Institucions: | 1Universidad Nacional Autónoma de México, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, México, Distrito Federal. México 2Universidad Nacional Autónoma de México, Instituto de Física, México, Distrito Federal. México |
| Any: | 2015 |
| Període: | May-Jun |
| Volum: | 61 |
| Número: | 3 |
| Paginació: | 196-206 |
| País: | México |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Analítico, teórico |
| Resumen en inglés | A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as the curl of a vector potential, which will then satisfy Poisson's equation with vorticity as a source term. In regions with zero vorticity, Poisson's equation reduces to Laplace's equation, and this allows for the construction of harmonic potentials inside and outside circles and ellipses, depending on the coordinate system. The vector potential is normal to the coordinate plane, and is proportional to the scalar harmonic functions on the plane, thereby guaranteeing that the velocity field is also harmonic and is located on the coordinate plane. The components of the velocity field normal to either a circle or an ellipse are continuous, but the tangential components are discontinuous, so that, in effect, a vortex sheet is introduced at these boundaries. This discontinuity is a measure of the vorticity, normal to the plane and distributed harmonically along the perimeter of the respective circles or ellipses. An analytic expression for the streamlines is obtained which makes visualisation of vortices of various geometries and harmonicities possible. This approach also permits a reformulation of the notion of multipolarity of vortices in the traditional sense of a multipolar expansion of the Green function for Poisson's equation. As an example of the applicability of this formulation to known vortical structures, Rankine vortices of different geometries are expressed in terms of harmonic functions |
| Disciplines | Física y astronomía |
| Paraules clau: | Física, Fluido incompresible, Vórtices estables, Ecuaciones de Euler, Superintegrabilidad, Solubilidad exacta |
| Keyword: | Physics and astronomy, Physics, Incompressible fluid, Steady vortices, Euler equations, Superintegrability, Exact solvability |
| Text complet: | Texto completo (Ver PDF) |
