Solution
= Solution
Using the polar-coordinate <curl> with $u_\theta=r\Omega(r)$ gives
$$
\boxed{
\boldsymbol\omega=\nabla\times\mathbf u
=\left(2\Omega+r\frac{d\Omega}{dr}\right)\mathbf e_z}.
$$
= Solution
Using the polar-coordinate <curl> with $u_\theta=r\Omega(r)$ gives
$$
\boxed{
\boldsymbol\omega=\nabla\times\mathbf u
=\left(2\Omega+r\frac{d\Omega}{dr}\right)\mathbf e_z}.
$$