An Etymological Dictionary of the German Language/Wanne
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Wanne, f., ‘winnowing fan,’ from the equiv. MidHG. wanne, OHG. wanna, f. As in the case of Wall, it is quite possible that the word was borrowed from Lat. (vannus, ‘winnowing fan’). There exists, however, a genuine Teut. stem from which Wanne can be derived. Goth. winþjan, and the equiv. E. winnow (from AS. windwian) point to a Teut. root winþ, ‘to winnow’ (Lat. ventilare), and hence OHG. wanna might stand for *wanþna. In that case the primit. kinship with Lat. vannus (from which E. fan is borrowed) would be conceivable.