  In two dimensional turbulence, vortex thinning process is one of the
attractive mechanism to explain inverse energy cascade in terms of vortex
dynamics. 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. The aim of this paper is to analyze the
vortex-thinning mechanism mathematically (using the incompressible Euler
equations), and give a mathematical evidence that large-scale vorticity gains
energy from small-scale vorticity due to the vortex-thinning process.

Analysis of PDEs;Fluid Dynamics