  The vorticity rotor field ${\bf B}=\mbox{rot}\,\mathbf{\omega}$
(di-vorticity) for freely decaying two-dimensional hydrodynamic turbulence due
to a tendency to breaking is concentrated in the vicinity of the lines
corresponding to the position of the vorticity quasi-shocks. The maximum value
of the di-vorticity $B_{max}$ at the stage of quasi-shocks formation increases
exponentially in time, while the thickness $\ell(t)$ of the maximum area in the
transverse direction to the vector ${\bf B}$ decreases in time also
exponentially. It is numerically shown that $B_{max} (t)$ depends on the
thickness according to the power law: $B_{max}(t)\sim \ell^{-\alpha}(t)$, where
the exponent $\alpha\approx 2/3$. This behavior indicates in favor of folding
for the divergence-free vector field of the di-vorticity.
