Lifting Line Theory and Helmholtz theorems

[Nimeo]

I was reasoning about prandtl's lifting line theory. Now, a lot of books state that if the the circulation changes across the bound vortex filament a vortex sheet of the same intensity must be shed from the filament following the wake. Is this a consequence of the helmolzt theorem that forbids any variation in circulation along a vortex filament, or not?

 

[K41]

Not sure, but it could also be due to Kelvin's theorem so that the net circulation over the entire region remains zero.