Fluid Dynamics | Part IB, 2004

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

Show that the flow field

u=(x,xω(t),z1)\mathbf{u}=(-x, x \omega(t), z-1)

has uniform vorticity of magnitude ω(t)=ω0et\omega(t)=\omega_{0} e^{t} for some constant ω0\omega_{0}.

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