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We have investigated the properties of gravito-turbulent discs in 3D usinghigh-resolution shearing-box simulations. For large enough domain sizes, $L_y\gtrsim 60H$, the disc settles down into a quasi-steady state, showing no longterm trends in properties or variation with box size. For smaller boxes, wefind that the azimuthal wavelength of the dominant spiral modes are limited tothe domain size. This is associated with a bursty behaviour that differs fromthe quasi-steady dynamics at larger sizes. We point out that a similartransition may be expected in global simulations at the point where the rangeof azimuthal wavelengths is limited by the finite disc size. This condition(i.e. when $60 H \sim 2 \pi R$, i.e. $H/R \sim 0.1$) correctly predicts thetransition to bursty behaviour previously found in global simulations fordisc-to-star mass ratios in excess of 0.25. We recover a transition in thedynamics from two- to three-dimensional behaviour, characterized by aturbulence that becomes more isotropic on small scales. This turbulence likelyplays an important role in the evolution of dust in self-gravitating discs,potentially dominating the collision velocity for particles with Stokes number$< 1$. Finally, we consider the stability of gravito-turbulence againstfragmentation, finding that discs which cool faster than a few dynamical timesfragment immediately, supporting previous results. We also find hints ofstochastic fragmentation at marginally longer cooling times, in which afragment forms from a quasi-equilibrium state. However, this makes littlepractical difference to region where planet formation via gravitationalinstability may occur.

Characterizing gravito-turbulence in 3D: turbulent properties and stability against fragmentation