Détermination analytique de potentiels d’écoulements non visqueux, incompressibles et bidimensionnels autour d’obstacles circulaires. (Analytical calculation of potentials for inviscid, incompressible, two- dimensional fluid flows around circular obstacles). (French) Zbl 0609.76014
This paper deals with a class of analytical functions called Abelian potentials, or Abelian integrals, attached to a Kleinean symmetric group, which represent exact solutions for particular problems. Given a grid of arbitrary circles of various radii, all separate from each other, these functions, solutions of the Laplace equations in a multiple-circle domain, describe all possible flows around the circle, in the case of incompressible irrotational inviscid two-dimensional flows: flow with logarithmic singularities (sources, vortex), with poles and with circulations around the obstacles. A series of results is given, showing streamlines for various cases.
MSC:
76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
22E70 | Applications of Lie groups to the sciences; explicit representations |
76M99 | Basic methods in fluid mechanics |