Evolution
The evolution of the vorticity field in time is described by the vorticity equation, which can be derived from the Navier-Stokes equations.
In many real flows where the viscosity can be neglected (more precisely, in flows with high Reynolds number), the vorticity field can be modeled well by a collection of discrete vortices, the vorticity being negligible everywhere except in small regions of space surrounding the axes of the vortices. This is clearly true in the case of 2-D potential flow (i.e. 2-D zero viscosity flow), in which case the flowfield can be modeled as a complex-valued field on the complex plane.
Vorticity is a useful tool to understand how the ideal potential flow solutions can be perturbed to model real flows. In general, the presence of viscosity causes a diffusion of vorticity away from the vortex cores into the general flow field. This flow is accounted for by the diffusion term in the vorticity transport equation. Thus, in cases of very viscous flows (e.g. Couette Flow), the vorticity will be diffused throughout the flow field and it is probably simpler to look at the velocity field than at the vorticity.
Read more about this topic: Vorticity
Famous quotes containing the word evolution:
“Analyze theory-building how we will, we all must start in the middle. Our conceptual firsts are middle-sized, middle-distanced objects, and our introduction to them and to everything comes midway in the cultural evolution of the race.”
—Willard Van Orman Quine (b. 1908)
“The evolution of a highly destined society must be moral; it must run in the grooves of the celestial wheels.”
—Ralph Waldo Emerson (1803–1882)
“Like Freud, Jung believes that the human mind contains archaic remnants, residues of the long history and evolution of mankind. In the unconscious, primordial “universally human images” lie dormant. Those primordial images are the most ancient, universal and “deep” thoughts of mankind. Since they embody feelings as much as thought, they are properly “thought feelings.” Where Freud postulates a mass psyche, Jung postulates a collective psyche.”
—Patrick Mullahy (b. 1912)