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

E. A. Kuznetsov; E. V. Sereshchenko

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arXiv · 1812.03752

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

E. A. Kuznetsov·E. V. Sereshchenko

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Abstract

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.

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E. A. Kuznetsov, E. V. Sereshchenko. 2018-12-10. Folding of the frozen-in-fluid di-vorticity field in two-dimensional hydrodynamic turbulence. https://arxiv.org/abs/1812.03752

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