4.I.8C

Write down the vorticity equation for the unsteady flow of an incompressible, inviscid fluid with no body forces acting.

Show that the flow field

$\mathbf{u}=(-x, x \omega(t), z-1)$

has uniform vorticity of magnitude $\omega(t)=\omega_{0} e^{t}$ for some constant $\omega_{0}$.

*Typos? Please submit corrections to this page on GitHub.*