Show that the vorticity transport equation can also be written as [frac{D omega}{D t}=v abla^{2} omega+[omega cdot

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Show that the vorticity transport equation can also be written as

\[\frac{D \omega}{D t}=v abla^{2} \omega+[\omega \cdot abla] \boldsymbol{v}\]

How does it simplify for 2D flows? How does it simplify for slow flows?

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