Solution
= Solution
For the stated incompressible planar flow, use the <stream function> convention $u=\psi_y$, $v=-\psi_x$. It gives $u_x+v_y=0$ and the <vorticity> is
$$
\nabla\times\mathbf u=(0,0,v_x-u_y)
=(0,0,-\psi_{xx}-\psi_{yy}).
$$
Thus $\boxed{\boldsymbol\omega=-\nabla^2\psi\,\hat{\mathbf z}}$, where the Laplacian is the two-dimensional one.