Folding in Two-dimensional Hydrodynamic Turbulence
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The vorticity rotor field B = rot ω (divorticity) 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 divorticity Bmax at the stage of quasishocks 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 Bmax(t) depends on the thickness according to the power law: Bmax(t) ~ ℓ−α(t), where the exponent α ≈ 2/3. This behavior indicates in favor of folding for the divergence-free vector field of the divorticity.
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