  We consider axisymmetric incompressible inviscid flows without swirl in
$\mathbb{R}^3$, under the assumption that the axial vorticity is non-positive
in the upper half space and odd in the last coordinate, which corresponds to
the flow setup for head-on collision of anti-parallel vortex rings. For any
such data, we establish monotonicity and infinite growth of the vorticity
impulse on the upper half-space. As an application, we achieve infinite growth
of Sobolev norms for certain classical/smooth and compactly supported vorticity
solutions in $\mathbb{R}^{3}$.
