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Vortex thinning is one of the main mechanisms of two-dimensional turbulence. By direct numerical simulation to the two-dimensional Navier–Stokes equations with small-scale forcing and large-scale damping, Xiao et al (2009 J. Fluid Mech. 619 1–44) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. On the other hand, Alexakis and Doering (2006 Phys. Lett. A 359 652–657) calculated the upper bound of the bulk averaged enstrophy dissipation rate of the steady-state two dimensional turbulence. In this paper, we show that vortex thinning induces enhanced dissipation with strictly slower vanishing order of the enstrophy dissipation than Re−1.

Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations