We study mass outflows driven from accretion discs by radiation pressure due to spectral lines. To investigate non-axisymmetric effects, we use the Athena++ code and develop a new module to account for radiation pressure driving. In 2D, our new simulations are consistent with previous 2D axisymmetric solutions by Proga et al. who used the Zeus 2D code. Specifically, we find that the disc winds are time dependent, characterized by a dense stream confined to $sim 45^{circ}$ relative to the disc midplane and bounded on the polar side by a less dense, fast stream. Introducing a vertical, $phi$-dependent, subsonic velocity perturbation in the disc midplane does not change the overall character of the solution but global outflow properties such as the mass, momentum and kinetic energy fluxes are altered by up to 100%. Non-axisymmetric density structures develop and persist mainly at the base of the wind. They are relatively small, and their densities can be a few times higher that the azimuthal average. The structure of the non-axisymmetric and axisymmetric solutions differ also in other ways. Perhaps most importantly from the observational point of view are the differences in the so called clumping factors, that serve as a proxy for emissivity due to two body processes. In particular, the spatially averaged clumping factor over the entire fast stream, while it is of a comparable value in both solutions, it varies about 10 times faster in the non-axisymmetric case.
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