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We start by exploiting the possibility of extracting the vorticity
from our 2-D measurement. Vorticity can be estimated by calculating
Several numerical schemes exist for performing this calculation, and three
different methods have been implemented in **MatPIV**. The first is
estimation by using Stokes theorem:
This approach integrates to find the circulation around a
point. Alternatively we can use a standard differentiation scheme,
such as forward or centered differences. **MatPIV** uses two
different and more accurate differential operators, namely least
squares and Richardson extrapolation. With the former of these schemes
the vorticity can be estimated by
while the latter uses
The major difference between the two last operators is that the
Richardson extrapolation is designed to produce a smaller truncation
error, while the least squares operator reduces the effect of
fluctuations. The latter reason is why the least squares operator is
often used with PIV measurements and is chosen as the default
calculation method in **MatPIV**.
The file *vorticity.m* calculates vorticity. Calling should look
like:

[vorticity]=vorticity(x,y,u,v,method).

Method should be one of 'centered', 'circulation', 'richardson' or
'leastsq', where the latter is the default. The former of the methods is
just an overloaded call to the MATLAB file curl.m (type *help curl*
at the command prompt). This file uses a centered differences approach
and will perform well if the velocities are smooth.
If no output argument is included, a figure window will appear showing
the result.

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Johan K. Sveen
2004-08-06