Drowse v. i. [imp. & p. p. Drowsed p. pr. & vb. n. Drowsing.]  To sleep imperfectly or unsoundly; to slumber; to be heavy with sleepiness; to doze. “He drowsed upon his couch.”
     In the pool drowsed the cattle up to their knees.   --Lowell.
  drowsing
       adj : half asleep; "made drowsy by the long ride"; "it seemed a
             pity to disturb the drowsing (or dozing) professor"; "a
             tired dozy child"; "the nodding (or napping)
             grandmother in her rocking chair" [syn: drowsy, drowsing(a),
              dozy]