Folding of the frozen-in-fluid di-vorticity field in two-dimensional hydrodynamic turbulence

Abstract

The vorticity rotor field ${\bf B}=\mbox{rot}\,\mathbfω$ (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 $\mathbf{B}$ 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 the exponent $\alpha \approx 2/3$. This behavior indicates in favor of folding for the divergence-free vector field of the di-vorticity.

5 pages, 5 figures