I just put up a new paper “Dynamics of Saturated Energy Condensation in Two-Dimensional Turbulence” on arXiv. Here is the abstract:
We derive and numerically confirm that the saturation of energy condensation in two-dimensional turbulence is governed by the balance between forcing and small-scale dissipation. The time scale of saturation is inversely proportional to the viscosity but the saturation energy level is determined by both viscosity and the forcing scale. It is shown that, because the energy dissipation is proportional to the enstrophy, which itself is a conserved quantity in the ideal case, it is necessary to resolve the enstrophy spectrum to achieve numerical consistency. We also find that the movement of the condensate vortices can be described as Brownian motion of an inertial particle.
The paper is also submitted to Physical Review E. Hopefully it will be accepted soon!