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Old   February 24, 2007, 10:38
Default vorticity
  #1
Marco
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Hello. The definition of vorticity, for curved closed streamlines,according to my understanding, is local spin, local rotation of a fluid parcel on its own axis.

The math definition is twice the angular velocity, but is it the angular velocity of whole fluid around a specified origin or the angular velocity of the fluid element on its own axis?

For example, a planet could orbit another bigger planet in a certain time, but orbit on itself at a much slower or faster speed, completing multiple revolution on itself in justone turn around the bigger planet. So, to me,for vorticity, we are talking about the angular velocity relative to the fluid element axis and not to the fixed origin.

thanks for any clarification.
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Old   February 25, 2007, 03:44
Default Re: vorticity
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Rami
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Marco,

The spin tensor, Wik, is defined as

2Wik = Ui,k - Uk,i

where Ui is the velocity vector.

From this, as only derivative are involved, it is evident that the spin is independent of the coordinate system location, i.e., if you transtate the origin by a constant, the spin is uneffected. Consequently, the spin is around the local rotation axis.

To further convince yourself, you may excercise a simple vortex in 2D: Ux=-V*sin(a), Uy=+Vcos(a), Uz=0, x=r*cos(a), y=r*sin(a), and then transtate the origin to (Xo, Yo, Zo).

I hope this helps.
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Old   March 9, 2007, 19:31
Default Re: vorticity
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Marco
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Rami,

thank you for the reply and expertise. Forgive again my trivial questions. I will learn at the end. 1) vorticity has the same units of angular velocity omega.If I find that the vorticity has a certain point, do I simply multiply its value by 2 to find the local angular velocity at that specific point, or is that legal only in rigid motion?

2)At the following website, towards the end, there are the four factors that determine a change in vorticity.

http://www.student.math.uwaterloo.ca/~amat361/Fluid%20Mechanics/topics/vorticity.htm

"Fluid layers of constant density (isopycnals) want to coincide with layers of constant pressure (isobars). If these layers do not coincide the fluid start to rotate to make them line up which causes vorticity to be generated. (in the example we start with zero vorticity."

Do you have a clearer explation of these four causes, especially the one I mention above?

thank you for any help

Marco

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