Folding in two-dimensional hydrodynamic turbulence

The vorticity rotor field $\mathbf{B}=\mathrm{curl}\omega$ (divorticity) for freely decaying two-dimensional hydrodynamic turbulence due to a tendency to breaking is concentrated near the lines corresponding to the position of the vorticity quasi-shocks. The maximum value of the divorticity $B_{\max}$ 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 $\mathbf{B}$ 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 $\alpha = 2/3$. This behavior indicates in favor of folding for the divergence-free vector field of the divorticity.