I came to this site looking for one word to describe the repeated flapping up and down of a sheet, blanket, (bed)spread, tablecloth, towel or whatever. Not having found such a definite one word, I would like to suggest the verb "to luff," as in [past tense]
She luffed the sheet over the bed until, at last, she let it slowly settle, edges and corners perfectly aligned as she intended.
In sailboat terminology (q.v.) "luffing""luffing" describes the repeated loose flapping of a sail caught in a direct head-on wind. Doesn't that sound right!? Even the fabric "snap" sound of a luffed "sheet" (whether sail or bed) sounds similar, n'est pas?
Therefore I think luffing is entirely suitable for describing the repeated flapping in the air (as in the wind for the towels on the beaches) of any cloth, and I will use it thusly henceforth (and perhaps copyright it for it's eventual widespread use in this context). Ahem. (c) Noone Atall.
Thanks for your indulgence ... and agreement.