Recent progress in understanding instability-driven turbulence in both two (2D) and three (3D) dimensions will be described. Turbulence in 3D is characterized by a forward transfer of energy, to small scales, while in 2D energy is transferred is in the opposite direction, towards larger scales. When driven by a prescribed stochastic force, the latter leads to the formation of large scale structures in the form of vortices or jets. When the turbulence is driven instead by a wavenumber-localized instability superposed on stochastic forcing, the inverse energy transfer may be arrested and no large scale condensate forms. We find that when a control parameter measuring the fraction of energy injected by the instability is increased, the system undergoes two transitions. Below a first threshold, a regular large-scale vortex condensate (LSC) forms. Crossing this threshold shielded vortices (SVs) emerge and coexist with the condensate. At a second threshold, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges, characterized by the preponderance of vortices of one sign only and suppressed inverse energy cascade. I will compare this 2D phenomenology with that observed in highly anisotropic but three-dimensional systems focusing on condensate formation in rapidly rotating Rayleigh-Benard convection via both reduced dynamics and direct numerical simulations of the Navier-Stokes equation.
