Kinetic energy of vortex rings

According to a standard textbook on fluid dynamics (Physical Hydrodynamics, Guyon et al., Oxford University Press, 2015), the order of magnitude of the velocity of a plane circular vortex ring of radius R (core radius $xill R$) in a fluid of density $rho$ is given by:

$Vapproxfrac{Gamma}{4pi R}Logleft(frac{R}{xi}right)$, here $Gamma$ is the circulation.

The kinetic energy is given by $E_kapproxrhoGamma^2frac{R}{2}Logleft(frac{R}{xi}right)$

These results are unusual in that an increase of the velocity results in a decrease in the kinetic energy (along with a decrease in the radius), which is the opposite of what one expects from particle mechanics. Is there a physical explanation for the above ?