Editing Vortex (section)

===Evolution===

Vortices need not be steady-state features; they can move and change shape. In a moving vortex, the particle paths are not closed, but are open, loopy curves like [[helix|helices]] and [[cycloid]]s. A vortex flow might also be combined with a radial or axial flow pattern. In that case the streamlines and pathlines are not closed curves but spirals or helices, respectively. This is the case in tornadoes and in drain whirlpools.  A vortex with helical streamlines is said to be [[solenoidal vector field|solenoidal]].

As long as the effects of viscosity and diffusion are negligible, the fluid in a moving vortex is carried along with it. In particular, the fluid in the core (and matter trapped by it) tends to remain in the core as the vortex moves about. This is a consequence of [[Helmholtz's second theorem]]. Thus vortices (unlike [[surface wave]]s and [[Longitudinal wave|pressure wave]]s) can transport mass, energy and momentum over considerable distances compared to their size, with surprisingly little dispersion. This effect is demonstrated by smoke rings and exploited in vortex ring [[vortex ring toy|toys]] and [[vortex ring gun|guns]].

Two or more vortices that are approximately parallel and circulating in the same direction will attract and eventually merge to form a single vortex, whose [[circulation (fluid dynamics)|circulation]] will equal the sum of the circulations of the constituent vortices. For example, an [[airplane wing]] that is developing [[lift (force)|lift]] will create a sheet of small vortices at its trailing edge. These small vortices merge to form a single [[wingtip vortices|wingtip vortex]], less than one [[chord (aircraft)|wing chord]] downstream of that edge.  This phenomenon also occurs with other active [[airfoil]]s, such as [[propeller]] blades.  On the other hand, two parallel vortices with opposite circulations (such as the two wingtip vortices of an airplane) tend to remain separate.

Vortices contain substantial energy in the circular motion of the fluid. In an ideal fluid this energy can never be dissipated and the vortex would persist forever. However, real fluids exhibit [[viscosity]] and this dissipates energy very slowly from the core of the vortex. It is only through dissipation of a vortex due to viscosity that a vortex line can end in the fluid, rather than at the boundary of the fluid.