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In the present work, vorticity has been calculated by choosing a small rectangular contour
around which the circulation is calculated from the velocity field using a numerical
integration scheme, such as trapezoidal rule. The local circulation is then divided by
the enclosed area to arrive at an average vorticity for the sub-domain. The following
formula provides a vorticity estimate at a point (i; j) based on circulation using eight
neighboring points (see Figure 3.32):
![](images/image163.png)
with
![](images/image164.png)
![](images/image165.png)
![](images/image166.png)
![](images/image167.png)
It has been observed from experiments that a circulation calculation via the velocity field
yields better estimates of vorticity, and in particular, the peak vorticity that is otherwise
under-predicted. At other locations, the vorticity field determined by the two approaches
are practically identical. The accuracy of the vorticity measurement from PIV data
depends on the spatial resolution of the velocity sampling and the accuracy of the velocity
measurements. Therefore, the vorticity error can be associated with calculation scheme
and the grid size used for velocity sampling. Another source of uncertainty is that
propagated from the velocity measurements. PIV velocity measurements are the local
averages of the actual velocity in the sense that it represents a low pass filtered version
of the actual velocity field. Thus, vorticity from PIV data is only a local average of an
already averaged velocity field and not a point measurement.
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