Equations used for vortex location and other postprocessing fields

[Visakh M G]

What equation does the vortex locator employ? Why is the range from 0 to 255? Also, Is there a documentation where I could see what equations are used in strain rate, shear rate, etc?

Thanks,

Visakh

[William Thielicke]

I think it is mentioned here:

https://groups.google.com/g/pivlab/c/GS30m95Ia1g/m/6GW_PLYPAgAJ

[Visakh M G]

Dear William,

I checked the discussion you mentioned, which redirects me to a paper "Stamhuis, E. J. (2006), Aquatic Ecology, 40(4), pp. 463–479.". I checked the definitions of Strain rate and shear rate in this paper, which seemed slightly odd to me. I checked the references metioned in that paper which lead me to Stamhuis and Videler 1995, J. Exp. Biol. 198: 283 – 294. Here again, the shear rate is defined as ∂v/∂x + ∂u/∂y and strain rate as ∂u/∂x - ∂v/∂y. I have also checked the references mentioned in that paper, which lead me to a paper in Ocean research, OKUBO, A. AND EBBESMEYER , C. C. (1976). Here again, the definitions are similar.

However, in classical fluid mechanics textbooks (kindly refer to section 3.4 in Fluid Mechanics by Cohen  and Kundu or section 2.4 of Viscous Fluid Flow by Papanastasiou or even Wikipedia https://en.wikipedia.org/wiki/Strain-rate_tensor), the strain rate tensor is defined as S = 1/2 (∇u + ∇u^T). The trace (sum of the diagonal elements) is the bulk /volumetric strain rate ∇.u = ∂u/∂x + ∂v/∂y for 2D case and is equal to the divergence of the velocity field. Again, the shear strain rate for 2D case is ∂v/∂x + ∂u/∂y, which is consistent with the shear rate in PIVLab. However, the strain rate in PIV Lab, which is defined according to the paper Stamhuis 2006 is ∂u/∂x - ∂v/∂y, and doesn't make any sense to me, nor could I find it in any of the classical textbooks of Fluid Mechanics including Batchelor.

I think a more appropriate way would be to refer to the "linear strain rates" as the diagonal components of the strain rate tensor i.e, for x-direction ∂u/∂x and for y-direction, ∂v/∂y separately. Their sum for 2D flows is the volumetric strain rate for compressible flows and is 0 for 2D incompressible flows. For 3D incompressible flows, this sum is -∂w/∂z. I don't know if there's any meaning to the definition of ∂u/∂x - ∂v/∂y as "strain rate"- which is actually a tensor quantity. Again, the shear rate could be renamed as shear strain rate, which I think is more appropriate.

Kindly correct me if I'm wrong, we can discuss.

Thanks,

Visakh

[William Thielicke]

Dear Visakh, thanks for your input. Could you please open an issue on GitHub and describe how the code would have to be changed in your opinion. Please also mention the references that you mentioned here.

I'll then change it in one of the coming releases and refer to the GitHub issue.

Thanks!

[Visakh M G]

Dear William,

I have opened an issue on GitHub:

https://github.com/Shrediquette/PIVlab/issues/82