verb

be half asleep; doze intermittently.

he was beginning to drowse in his chair

doze,sleep (lightly),nap,take a nap,catnap,take a siesta,rest,snooze,have a snooze,snatch/get forty winks,get some shut-eye,kip,have a kip,get some kip,catch some Zs,catch a few Zs,slumber