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After more research the connection appears to be ancient — G. schweifen and MHG. sweimen seem to be cognates, along with schweben, Ice. svifa, sveima, svima and English swim in the phrase "made my/his/her head swim". The word meaning "flood" you refer to above is probably just another application of the root — it seems to have described the fast swooping, sweeping, soaring, wandering, dizzying flight of a bird, and then by analogy and extension to the movement of flames, fast flowing water, scythes, brooms, people etc.