Evolution of vortex statistics in two-dimensional turbulence
Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density
of these vortices decays in time as ρ∼ t− ξ with ξ≊ 0.75. A new scaling theory is proposed
which expresses all statistical properties in terms of ξ. Thus the average circulation of the
vortices increases as t ξ/2 and their average radius as t ξ/4. The total energy is constant, the
enstrophy decreases as t− ξ/2, and the vorticity kurtosis increases as t ξ/2. These results are
supported both by numerical simulations of the fluid equations and by solutions of a …
of these vortices decays in time as ρ∼ t− ξ with ξ≊ 0.75. A new scaling theory is proposed
which expresses all statistical properties in terms of ξ. Thus the average circulation of the
vortices increases as t ξ/2 and their average radius as t ξ/4. The total energy is constant, the
enstrophy decreases as t− ξ/2, and the vorticity kurtosis increases as t ξ/2. These results are
supported both by numerical simulations of the fluid equations and by solutions of a …
Abstract
Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density of these vortices decays in time as ρ∼ t− ξ with ξ≊ 0.75. A new scaling theory is proposed which expresses all statistical properties in terms of ξ. Thus the average circulation of the vortices increases as t ξ/2 and their average radius as t ξ/4. The total energy is constant, the enstrophy decreases as t− ξ/2, and the vorticity kurtosis increases as t ξ/2. These results are supported both by numerical simulations of the fluid equations and by solutions of a modified point-vortex model.
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