From Longman Dictionary of Contemporary Englishdrowsedrowse /draʊz/ verb [intransitive] SLEEPto be in a light sleep or to feel as though you are almost asleep I was drowsing in front of the television when you called.→ See Verb table
Examples from the Corpus
drowse• Exhausted by their exercise, they were content to drowse in the sun.• We were content to drowse in the warm sunlight on the beach.• But the patient begins to drowse into a strange kind of sleep.• The two bureaucrats lay drowsing on the port and starboard cockpit seats.Origin drowse (1500-1600) drowsy 