Modelling the propagation of supernova (SN) bubbles, in terms of energy, momentum, and spatial extent, is critical for simulations of galaxy evolution which do not capture these scales. To date, small-scale models of SN feedback predict that the evolution of above-mentioned quantities can be solely parametrized by average quantities of the surrounding gas, such as density. However, most of these studies neglect the turbulent motions of this medium. In this paper, we study the propagation and evolution of SNe in turbulent environments. We confirm that the time evolution of injected energy and momentum can be characterized by the average density. However, the details of the density structure of the interstellar medium play a crucial role in the spatial extent of the bubble, even at a given average density. We demonstrate that spherically symmetric models of SN bubbles do not model well their spatial extent, and therefore cannot not be used to design sub-grid models of SNe feedback at galactic and cosmological scales
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