  Rotating turbulence is commonly known for being dominated by geostrophic
vortices that are invariant along the rotation axis and undergo inverse
cascade. Yet, it has recently been shown to sustain fully three-dimensional
states with a downscale energy cascade. In this letter, we investigate the
statistical properties of three-dimensional rotating turbulence by the means of
direct numerical simulations in a triply periodic box where geostrophic
vortices are specifically damped. The resulting turbulent flow is an inertial
wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived
analytically by Galtier (Phys. Rev. E, 68, 2003), thus offering numerical proof
of the relevance of wave turbulence theory for three-dimensional, anisotropic
waves. Lastly, we show that the same forcing leads to either geostrophic or
wave turbulence depending on the initial condition. Our results thus bring
further evidence for bi-stability in rotating turbulent flows.
