# Vorticity magnitude

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 January 19, 2005, 05:25 Vorticity magnitude #1 CFD-junior Guest   Posts: n/a Please could someone tell me how to calculate the vorticity magnitude. Thanks mohammad_mec87 likes this.

 January 19, 2005, 10:04 Re: Vorticity magnitude #2 ag Guest   Posts: n/a Compute the curl of velocity and take the magnitude of the vector. mohammad_mec87 likes this.

 January 20, 2005, 14:21 Re: Vorticity magnitude #3 agg Guest   Posts: n/a wx = dw/dy - dv/dz wy = du/dz - dw/dx wz = dv/dx - du/dy w = wx(i) + wy(j) + wz(k) vorticity magnitude = sqrt(w.w) = sqrt( wx*wx +wy*wy +wz*wz) mohammad_mec87 likes this.

 January 21, 2005, 22:59 Re: Vorticity magnitude #4 w0er Guest   Posts: n/a Could this function be defined into any cfd post.

 August 17, 2011, 10:07 or with vorticity tensor #5 Member   Join Date: May 2010 Posts: 44 Rep Power: 9 |w|=||wij|| where wij is the vorticity tensor defined as the antysymmetric part of the velocity gradient tensor. Its magnitude defined by: ||wij||=sqrt(2wij*wij) and its the same as the magnitude of the vorticity vector as defined earlier. mohammad_mec87 likes this.

March 2, 2016, 01:01
#6
New Member

Hanxun Yao
Join Date: Feb 2016
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Quote:
 Originally Posted by la7low |w|=||wij|| where wij is the vorticity tensor defined as the antysymmetric part of the velocity gradient tensor. Its magnitude defined by: ||wij||=sqrt(2wij*wij) and its the same as the magnitude of the vorticity vector as defined earlier.

Hi,

If I define a antisymmetric matrix as:
0 x y
-x 0 z = A
-y -z 0
which is similar to Vorticity tensor, but when I calculate A*A, I got
-2*x^2-2*y^2-2*z^2 which is negative and has problem under square root. Could you please tell what causes this problem. Thank you very much.

March 2, 2016, 04:33
#7
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,643
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Quote:
 Originally Posted by Hanseny Hi, If I define a antisymmetric matrix as: 0 x y -x 0 z = A -y -z 0 which is similar to Vorticity tensor, but when I calculate A*A, I got -2*x^2-2*y^2-2*z^2 which is negative and has problem under square root. Could you please tell what causes this problem. Thank you very much.

I do not understand what you did ... if you want to define a measure for a matrix, you should define some norm on that ||A||, this is not so simple.

You can define an induced norm by using a (non vanishing) vector x such that
||A.x||/||x||

March 2, 2016, 07:04
#8
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Hanxun Yao
Join Date: Feb 2016
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Quote:
 Originally Posted by FMDenaro I do not understand what you did ... if you want to define a measure for a matrix, you should define some norm on that ||A||, this is not so simple. You can define an induced norm by using a (non vanishing) vector x such that ||A.x||/||x||

Now I know what is the norm of a matrix, then I still have a question:

What is the magnitude of vorticity, seems like it is not equal to the norm

of vorticity tensor. thanks again.

March 2, 2016, 07:11
#9
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,643
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Quote:
 Originally Posted by Hanseny Thank you for your reply, Now I know what is the norm of a matrix, then I still have a question: What is the magnitude of vorticity, seems like it is not equal to the norm of vorticity tensor. thanks again.

Indeed the vorticity vector must be extractet from the antisymmetric matrix..

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