Vorticity

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Vorticity is a mathematical concept used in fluid dynamics. It can be related to the amount of "circulation" or "rotation" (or more strictly, the local angular rate of rotation) in a fluid.

The average vorticity in a small region of fluid flow is equal to the circulation \Gamma around the boundary of the small region, divided by the area A of the small region.

\omega_{av} = \frac {\Gamma}{A}


Notionally, the vorticity at a point in a fluid is the limit as the area of the small region of fluid approaches zero at the point:

 \omega = \frac {d \Gamma}{dA}


Mathematically, the vorticity at a point is a vector and is defined as the curl of the velocity:


\vec \omega = \vec \nabla \times \vec v .


In the field of flow of a fluid, vorticity \omega is zero almost everywhere. It is only in special places, such as the boundary layer or the core of a vortex, that the vorticity is not zero.

Further reading[change | edit source]

  • Batchelor, G. K., (1967, reprinted 2000) An Introduction to Fluid Dynamics, Cambridge Univ. Press
  • Ohkitani, K., "Elementary Account Of Vorticity And Related Equations". Cambridge University Press. January 30, 2005. ISBN 0-521-81984-9
  • Chorin, Alexandre J., "Vorticity and Turbulence". Applied Mathematical Sciences, Vol 103, Springer-Verlag. March 1, 1994. ISBN 0-387-94197-5
  • Majda, Andrew J., Andrea L. Bertozzi, "Vorticity and Incompressible Flow". Cambridge University Press; 2002. ISBN 0-521-63948-4
  • Tritton, D. J., "Physical Fluid Dynamics". Van Nostrand Reinhold, New York. 1977. ISBN 0-19-854493-6
  • Arfken, G., "Mathematical Methods for Physicists", 3rd ed. Academic Press, Orlando, FL. 1985. ISBN 0-12-059820-5

Other websites[change | edit source]