"be heavy with sleep, be half asleep," 1570s, probably a back-formation from drowsy. Old English had a similar word, but there is a 600-year gap. Related: Drowsed; drowsing.The noun meaning "state of being half asleep" is by 1814.
drought
drove
drover
droves
drown
drowse
drowsy
drub
drubbing
drudge
drudgery