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More simply, vortex lines move with the fluid. Also vortex lines and tubes must appear as a closed loop, extend to infinity or start/end at solid boundaries. Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have application in understanding: Generation of lift on an airfoil; Starting vortex; Horseshoe vortex
In general, vortex lines (in particular, the axis line) are either closed loops or end at the boundary of the fluid. A whirlpool is an example of the latter, namely a vortex in a body of water whose axis ends at the free surface. A vortex tube whose vortex lines are all closed will be a closed torus-like surface.
The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an irrotational (potential or free) vortex. However, in a potential vortex, the velocity becomes infinite at the vortex center.
In particular, simple potential flows (called elementary flows) such as the free vortex and the point source possess ready analytical solutions. These solutions can be superposed to create more complex flows satisfying a variety of boundary conditions.
For free vortices and other bodies outside one body without bound vorticity and without vortex production, a generalized Lagally theorem holds, [13] with which the forces are expressed as the products of strength of inner singularities (image vortices, sources and doublets inside each body) and the induced velocity at these singularities by all ...
Streamlines for the potential flow around a spinning cylinder. The concentric circular streamlines of a free vortex have been superimposed on the parallel streamlines of a uniform flow. Streamlines are closer spaced immediately above the cylinder than below, so the air flows faster past the upper surface than past the lower surface.
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No. A vortex that involves no shear and so does not require a torque to maintain it is known as a 'free vortex' and velocity is inversely proportional to radius. A vortex that involves shear and requires a torque to maintain it is a 'forced vortex' and velocity is proportional to radius. Dolphin51 12:42, 22 December 2008 (UTC)