The above Atchafalaya essay is eye opening about the Mississippi River and how its natural course has swayed back and forth hundreds of miles over the centuries. We have now decided these two rivers should stop moving, but the earth doesn't see it that way. When they hit the gulf, their flow speed lowers, dropping the carried sediment. This causes their mouth to move slightly to an area with less dropped sediment. Humans have built walls attempting to constrain movement, but that may be a long-term losing battle.
Recommended reading, and a nice entry point to McPhee if you haven't read him yet.