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Vorticity is a mathematical concept used in fluid dynamics. It can be related to the amount of "circulation" or "rotation" in a fluid.
In fluid dynamics, vorticity is the curl of the fluid velocity. It can also be considered as the circulation per unit area at a point in a fluid flow field. It is a vector quantity, whose direction is along the axis of the fluid's rotation. For a two-dimensional flow, the vorticity vector is perpendicular to the plane.
For a fluid having locally a "rigid rotation" around an axis (i.e., moving like a rotating cylinder), vorticity is twice the angular velocity of a fluid element. An irrotational fluid is one whose vorticity=0. Somewhat counter-intuitively, an irrotational fluid can have a non-zero angular velocity (e.g. a fluid rotating around an axis with its angular velocity inversely proportionnal to the distance to the axis has a zero vorticity).
One way to visualize vorticity is this: consider a fluid flowing. Imagine that some tiny part of the fluid is instantaneously rendered solid, and the rest of the flow removed. If that tiny new solid particle would be rotating, rather than just translating, then there is vorticity in the flow.
In the atmospheric sciences, vorticity is a property that characterizes large-scale rotation of air masses. Since the atmospheric circulation is nearly horizontal, the (3 dimensional) vorticity is nearly vertical, and it is common to talk use the vertical component as the scalar vorticity. The scalar vorticity is positive when the parcel has a counterclockwise rotation for the Northern Hemisphere. It is negative when the parcel has clockwise rotation for the Northern Hemisphere. 
for relative vorticity and
The barotropic vorticity equation is the simplest way for forecasting the movement of Rossby waves (that is, the troughs and ridges of 500 mb geopotential) over a limited amount of time (a few days). In the 1950s, the first successful programs for numerical weather forecasting utilized that equation.
Vorticity is important in many other areas of fluid dynamics. For instance, the lift distribution over a finite wing may be approximated by assuming that each segment of the wing has a semi-infinite trailing vortex behind it. It is then possible to solve for the strength of the vortices using the criterion that there be no flow induced through the surface of the wing. This procedure is called the vortex panel method of computational fluid dynamics. The strengths of the vortices are then summed to find the total approximate circulation about the wing. Lift is the product of circulation, airspeed, and air density.
- Main : Application of tensor theory in engineering science, Barotropic vorticity equation, D'Alembert's paradox, Vortex, Vortical, Vorticity equation, Vortical motion
- Atmospheric sciences : Prognostic variable
- Fluid dynamics: Biot-Savart Law, Circulation, Curl, Navier-Stokes equations
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- Parker, Douglas, "ENVI 2210 - Atmosphere and Ocean Dynamics, 9: Vorticity". School of the Environment, University of Leeds. September 2001.
- Graham, James R., "Astronomy 202: Astrophysical Gas Dynamics". Astronomy Department, UC, Berkeley.
- "Spherepack 3.1". (includes a collection of FORTRAN vorticity program)
- "Mesoscale Compressible Community (MC2) Real-Time Model Predictions". (Potential vorticity analysis)
- "Vorticity" images via Google.
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