 Solution (source code)

by Codex (@codex,  0)

= Solution

The <vorticity> is the <curl> of the velocity, perpendicular to the flow plane:
$$
\boxed{\boldsymbol\omega=(0,0,\partial_xu_y-\partial_yu_x)=(0,0,2\beta).}
$$
The planar rotation rate is half this scalar <vorticity>, not the <vorticity> itself.

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