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VORTICITY AND VORTICITY EQUATION

VORTICITY AND VORTICITY EQUATION. Vorticity is the tendency of fluid elements to rotate. http://mathicse.epfl.ch/~foureste/. A property of vorticity:. Vorticity vector:. Just as streamlines were defined to be lines that are everywhere parallel to the velocity vector

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VORTICITY AND VORTICITY EQUATION

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  1. VORTICITY AND VORTICITY EQUATION Vorticity is the tendency of fluid elements to rotate http://mathicse.epfl.ch/~foureste/

  2. A property of vorticity: Vorticity vector:

  3. Just as streamlines were defined to be lines that are everywhere parallel to the velocity vector vortex lines are defined to be everywhere parallel to the vorticity vector.

  4. CIRCULATION Another measure of the tendency of fluid elements to rotate Stokes’ theorem: normal flux of vorticity through a cross section of a vortex tube (of area A) = line integral of tangential velocity around it. For an inviscid fluid, Kelvin’s theorem states that

  5. For Couette Flow  z H vortex lines are in theydirection and equidistant

  6. For Poseuille Flow

  7. Vortex Tubes off Flagler Beach http://www.srh.noaa.gov/jax/?n=waterspouts http://www.floridahurricanelawfirm.com/labels/Hurricane%20Property%20Damage.html

  8. THE VORTICITY EQUATION Obtained by taking the curl of: Can use the vector identity (Lecture 7): LHS only: Because the curl of a gradient = 0

  9. = 0 for incompressible flows RHS only:

  10. Including Earth’s rotation effects: Stretching and tilting of vortex lines Isobars and isopycnals not parallel -- baroclinicity diffusion

  11. Stretching and tilting of vortex lines Spatial gradient in the direction of vorticity If velocity is not constant in the direction of vorticity, the vortex lines will be distorted, i.e., strained -- increased vorticity with vortex stretching This term is absent in 2-D flows where vorticity is perpendicular to the plane of the flow, e.g., Couette & Poiseuille flows. Water Spout (Lake Buchanan, Texas) Whirlpool (la Rance, France)

  12. Blue Holes Bahamas http://synaesthetical.blogspot.com/2010/07/blue-holes-of-bahamas-wes-c-skiles.html

  13. Baroclinic Generation geopotential surface isobars isopycnals z increasing depth and density x

  14. Turbulence is characterized by fluctuating vorticity in structures -- EDDIES. http://mathicse.epfl.ch/~foureste/

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