Abstract
The statistical balance between self-amplification of the vorticity gradient (VG) and viscous smoothing in two-dimensional turbulence is considered. A closed exact equation for the conditionally averaged VG (with fixed VG in a certain point) is derived from the Navier-Stokes equation. A family of solutions of this equation is obtained. Solutions depend non-analytically on the fixed VG, due to the effect of self-amplification. The conditionally averaged vorticity field and high order two-point moments of the VG are calculated. These results can be verified by numerical experiments. The developed method, based on the conditional averaging of the equation for the local characteristic of motion, can be applied to a variety of physical systems with strong interaction, including magnetized plasma.
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