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 CFD-junior January 19, 2005 05:25

Vorticity magnitude

Please could someone tell me how to calculate the vorticity magnitude.

Thanks

 ag January 19, 2005 10:04

Re: Vorticity magnitude

Compute the curl of velocity and take the magnitude of the vector.

 agg January 20, 2005 14:21

Re: Vorticity magnitude

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)

 w0er January 21, 2005 22:59

Re: Vorticity magnitude

Could this function be defined into any cfd post.

 la7low August 17, 2011 10:07

or with vorticity tensor

|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.

 Hanseny March 2, 2016 01:01

Quote:
 Originally Posted by la7low (Post 320482) |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.

 FMDenaro March 2, 2016 04:33

Quote:
 Originally Posted by Hanseny (Post 587644) 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||

 Hanseny March 2, 2016 07:04

Quote:
 Originally Posted by FMDenaro (Post 587663) 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.

 FMDenaro March 2, 2016 07:11

Quote:
 Originally Posted by Hanseny (Post 587678) 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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