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There are numerous functions that calculate vorticity. The majority are calculated using spherical harmonics, and as such they require the data to be global, with no missing values. These routines include:

The last function uv2vr_cfd does not require global extent or no missing data, but it does require that the lat/lon coordinates of the data be one dimensional. It does not work, therefore, with POP ocean data or any other grid that has 2D lat/lon coordinates. The "cfd" in the name stands for centered finite difference.
vort_1.ncl: Calculates vorticity given u and v.

uv2vrG uses Spherepack to compute vorticity given u and v wind components. It requires that the data be global and contain no missing data.

uv2vrG_Wrap is a wrapped version of this function that retains meta data.