...also known as postprandial sleepiness...It kinda depends on the content of the meal. Meals heavy in starches and carbohydrates produce more and faster sleepiness than those containing more protein. One site suggests that there is a chemical in our brain which slows down nerve activity and induces sleep. This chemical is called serotonin. There is a naturally occurring amino acid which is the raw material out of which serotonin is made. This amino acid is called tryptophan. Tryptophan is often used to treat poor sleep. It takes about one hour for tryptophan to enter the brain and be converted into serotonin.
Tryptophan occurs naturally in turkey, for example and is one of the reasons, shown scientifically, that we here in the U.S. experience this phenomena at Thanksgiving, having consumed large amounts of the bird. Additionally, the large amounts of blood diverted to the digestive system contributes to the drowsiness...
(Apparently this site is having difficulty with longer posts, hence the two-parter)