  In two-dimensional forced Navier-Stokes turbulence, energy cascades to the
largest scales in the system to form a pair of coherent vortices known as the
Bose condensate. We show, both numerically and analytically, that the energy
condensation saturates and the system reaches a statistically stationary state.
The time scale of saturation is inversely proportional to the viscosity and the
saturation energy level is determined by both the viscosity and the force. We
further show that, without sufficient resolution to resolve the small-scale
enstrophy spectrum, numerical simulations can give a spurious result for the
saturation energy level. We also find that the movement of the condensate is
similar to the motion of an inertial particle with an effective drag force.
Furthermore, we show that the profile of the saturated coherent vortices can be
described by a Gaussian core with exponential wings.
