That's wonderful. Thank you.
OK, Kelvin theorem doesn't say that per se, but it is implied. It says:
For barotropic fluid, i.e. fluid where ##\rho## is a function of only ##p##
##\frac{D\Gamma}{Dt} = \frac{D}{Dt}(\oint \vec{v} \,dl ) = 0##
After some manipulations, mainly inserting Newton's...