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Vorticity magnitude

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Old   January 19, 2005, 05:25
Default Vorticity magnitude
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Please could someone tell me how to calculate the vorticity magnitude.

Thanks
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Old   January 19, 2005, 10:04
Default Re: Vorticity magnitude
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Compute the curl of velocity and take the magnitude of the vector.
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Old   January 20, 2005, 14:21
Default Re: Vorticity magnitude
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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)

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Old   January 21, 2005, 22:59
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Could this function be defined into any cfd post.
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Old   August 17, 2011, 10:07
Default or with vorticity tensor
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|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.
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Old   March 2, 2016, 01:01
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Quote:
Originally Posted by la7low View Post
|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.
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Old   March 2, 2016, 04:33
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Quote:
Originally Posted by Hanseny View Post
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||
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Old   March 2, 2016, 07:04
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Originally Posted by FMDenaro View Post
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||


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.
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Old   March 2, 2016, 07:11
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Filippo Maria Denaro
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Originally Posted by Hanseny View Post
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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