Vorticity equations of incompressible Navier-Stokes equations in 2D

Question

We know for incompressible Navier-Stokes equations, we have the vorticity equation: $$\omega_t - \Delta \omega + (u \cdot \nabla)\omega = (\omega \cdot \nabla)u$$

But for two dimensional space, $(u \cdot \nabla)\omega $. I don't see why after I plug in the expression of $\omega$. (Here $\omega = \partial_1 u_2 - \partial_2 u_1$)

Answer 1

In 2D case, the vorticity is a scalar, and the vortex stretching term $\omega\cdot\nabla u$ should disappear.