Motion of vortex sources on a plane and a sphere
نویسندگان
چکیده
The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Particular solutions analogous to the homothetic configurations in celestial mechanics are given.
منابع مشابه
ar X iv : n lin / 0 50 70 57 v 1 [ nl in . S I ] 2 6 Ju l 2 00 5 REDUCTION AND CHAOTIC BEHAVIOR OF POINT VORTICES ON A PLANE AND A SPHERE
We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given in more detail. We also use the Poincaré surface-of-section technique to perform the reduction a four-vortex...
متن کاملM ar 2 00 5 DYNAMICS AND STATICS OF VORTICES ON A PLANE AND A SPHERE —
In the present paper a description of a problem of point vortices on a plane and a sphere in the " internal " variables is discussed. The Hamiltonian equations of motion of vortices on a plane are built on the Lie–Poisson algebras, and in the case of vortices on a sphere on the quadratic Jacobi algebras. The last ones are obtained by deformation of the corresponding linear algebras. Some partia...
متن کاملThe motion of point vortices on closed surfaces
We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is non-zero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the Laplace–Beltrami operator must vanish). On variable Gaussian curvature surfaces, this re...
متن کاملNew Periodic Solutions for Three or Four Identical Vortices on a Plane and a Sphere
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics. 1 Equations of motion and first integrals for vortices on a plane For n point vortices with Cartesian coordinates (xi, yi) and intensities Γi, the Hamiltonian equations of the motion are Γiẋi = ∂H ∂yi , Γi...
متن کاملOn Coherent Structures of Turbulent Open-channel Flow Above a Rough Bed
Present study examines turbulent structures of a rough bed open-channel flow in the context of deterministic approach. Instantaneous velocity field is measured in different hydraulic conditions using two dimensional Particle Image Velocimetry (PIV) in vertical plane and Stereoscopic PIV in horizontal plane. Different techniques and quantities such as swirl strength, two-point and cross-correlat...
متن کامل