  In many geophysical and astrophysical flows, suppression of fluctuations
along one direction of the flow drives a quasi-2D upscale flux of kinetic
energy, leading to the formation of strong vortex condensates at the largest
scales. Recent studies have shown that the transition towards this condensate
state is hysteretic, giving rise to a limited bistable range in which both the
condensate state as well as the regular 3D state can exist at the same
parameter values. In this work, we use direct numerical simulations of
thin-layer flow to investigate whether this bistable range survives as the
domain size and turbulence intensity are increased. By studying the time scales
at which rare transitions occur from one state into the other, we find that the
bistable range grows as the box size and/or Reynolds number Re are increased,
showing that the bistability is neither a finite-size nor a finite-Re effect.
We furthermore predict a crossover from a bimodal regime at low box size, low
Re to a regime of pure hysteresis at high box size, high Re, in which any
transition from one state to the other is prohibited at any finite time scale.
