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In Mathematics, and in particular Fluid Mechanics, the point vortex system is a well-studied dynamical system consisting of a number of points on the plane (or other surface) moving according to a law of interaction that derives from fluid motion. It was first introduced by Hermann von Helmholtz[1] in 1858, as part of his investigation into the motion of vortex filaments in 3 dimensions. It was first written in Hamiltonian form by Gustav Kirchhoff[2] a few years later.
A single vortex in a fluid is like a whirlpool, with the fluid rotating about a central point (the point vortex). The speed of the fluid is inversely proportional to the distance of a fluid element to the point vortex. The constant of proportionality (or it divided by 2π) is called the vorticity or vortex strength of the point vortex. This is positive if the fluid rotates anticlockwise (like a cyclone in the Northern hemisphere) or negative if it rotates clockwise (anticyclone in the N. hemisphere), and has a constant value for each point vortex.
It was realized by Helmholtz that if there are several point vortices in an ideal fluid, then the motion of each depends only on the positions and strengths of the others, thereby giving rise to a system of ordinary differential equations whose variables are the coordinates of the point vortices (as functions of time).
The study of point vortices has been called a Classical Mathematics Playground by the fluid dynamicist Hassan Aref (2007), due to the many areas of classical mathematics that can be brought to bear for the analysis of this dynamical system.