Folding in Two-dimensional Hydrodynamic Turbulence

The vorticity rotor field B = curlω (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 ℓ(t) of the maximum area in the transverse direction to the vector 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) ∼ ℓ ^−α (t), where α = 2/3. This behavior indicates in favor of folding for the divergence-free vector field of the divorticity.