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Atmospheric flows display self-organization processes or patter formation at all scales, from scales associated with small-scale turbulence to planetary scales. In this talk we will present results from numerical simulations in two different atmospheric contexts: The case of dry atmospheres at mesoscales, with a special focus on self-organization processes, and the case of volcanic eruptions with a special focus on particle clustering and patter formation. In the former case, these processes lead to the formation of ring-like structures, which through electrification processes can lead to ring-shaped thunderstorms as recently observed in the Hunga Tonga–Hunga Haʻapai volcanic eruption.