  We examine the steady state of turbulent flows in thin layers using direct
numerical simulations. It is shown that when the layer thickness is smaller
than a critical height, an inverse cascade arises which leads to the formation
of a steady state condensate where most of the energy is concentrated in the
largest scale of the system. For layers of thickness smaller than a second
critical height, the flow at steady state becomes exactly two-dimensional. The
amplitude of the condensate is studied as a function of layer thickness and
Reynolds number. Bi-stability and intermittent bursts are found close to the
two critical points. The results are interpreted based on a mean field
three-scale model that reproduces some of the basic features of the numerical
results.
