Use 'drowse' to describe a state between being awake and asleep, showing someone isn't fully alert. She tried to concentrate on the lecture but found herself drowsing in the warm classroom.
Pro Tip 2/3
Physical Activity
'Drowse' can imply physical inactivity and suggest a relaxed posture or environment. Under the shade of the tree, he drowsed comfortably in the hammock.
Pro Tip 3/3
Gradual Onset
The act of 'drowsing' often gradually happens as sleepiness takes over, generally unplanned. As the train gently rocked back and forth, she found herself drowsing off.