# Definition of vorticity and strain rate in paraview

Folks,

I’m attempting to get skin friction on a wall in paraview, and see two possible functions I could use to obtain this. What I’m really wondering is what the actual definition of these functions are.

When I read in the CFD solution, I can ask for vorticity to be calculated (as a vector). What I’d really like is the strain rate tensor, but in a thin shear layer/boundary layer where the derivatives in one direction are orders of magnitude higher in one direction, the magnitude of the strain rate tensor and the vorticity tensor are nearly the same, so I think I need to use this.

I’m asuming that for curvilinear grids, the vorticity is correctly calculated, but want to know where I can find this information. I am assuming that

\omega_x = 0.5*(\partial_z velocity_y - \partial_y velocity_z)
\omega_y = 0.5*(\partial_x velocity_z - \partial_z velocity_x)
\omega_z = 0.5*(\partial_y velocity_x - \partial_x velocity_y)


(where \partial_n is the partial differential operator in the “n” direction).

Is this true? Is this usable somehow on unstructured grids? Is there a way to get derivatives directly with the calculator?

I’ve checked the FAQ, searched here, and did google searches, but I’m not finding anything. What I’m really wondering about is where I can dig out what exactly these function definitions (like vorticity) are actually defined.

Thanks much,
Mike

And here, I think I’ve got a factor of 1/2 off, possibly in moving from the tensor to the vector form? I think what is coded may well be

\omega_x = \partial_z velocity_y - \partial_y velocity_z
\omega_y = \partial_x velocity_z - \partial_z velocity_x
\omega_z = \partial_y velocity_x - \partial_x velocity_y