Galactic outflows, driven by active galactic nuclei (AGN), play a crucial role in galaxy formation and in the self-regulated growth of supermassive black holes (BHs). AGN feedback couples to and affects gas, rather than stars, and in many, if not most, gas-rich galaxies cold gas is rotationally supported and settles in a disc. We present a 2D analytical model for AGN-driven outflows in a gaseous disc and demonstrate the main improvements, compared to existing 1D solutions. We find significant differences for the outflow dynamics and wind efficiency. The outflow is energy-driven due to inefficient cooling up to a certain AGN luminosity ($\sim 10^{43}$erg/s in our fiducial model), above which the outflow remains momentum-driven in the disc up to galactic scales. We reproduce results of 3D simulations that gas is preferentially ejected perpendicular to the disc and find that the fraction of ejected interstellar medium is lower than in 1D models. The recovery time of gas in the disc, defined as the freefall time from the radius to which the AGN pushes the ISM at most, is remarkably short, of the order 1Myr. This indicates that AGN-driven winds cannot suppress BH growth for long. Without the inclusion of supernova feedback, we find a scaling of the black hole mass with the halo velocity dispersion of $M_\mathrm{BH} \propto σ^{4.8}$.

22 pages, 22 figures, published in MNRAS