By direct numerical simulation to the two-dimensional Navier-Stokes equations with small-scale forcing and large-scale damping, Xiao-Wan-Chen-Eyink (2009) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. On the other hand, Alexakis-Doering (2006) calculated 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 $Re^{ -1}$.}
Categories: math.AP physics.flu-dyn