Graduate Question about Kelvin’s circulation theorem

[Seyn]

In Currie’s fluid mechanics textbook, there is a statement “the vorticity of each fluid particle will be preserved.” as the result of Kelvin’s circulation theorem.
Kelvin’s circulation theorem claims that
For inviscid flow, constant density or barotropic fluid, conservative body force,
the circulation around an arbitrary contour is conserved following same fluid particle.
Does Kelvin’s theorem also guarantee the vorticity on each fluid particles? Why?

 

[pasmith]

Take a look at the vorticity equation under the same conditions as Kelvin's circulation theorem. Does it reduce to \frac{D\omega}{Dt} = 0?