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'Delta switching', also known as 'avulsion', is the process by which some rivers - such as the Mississippi River - change their course near their deltas.
The flow of a river is controlled by its gradient, which decreases as it nears the ocean, becoming nearly zero at the delta's toe.^[1] Eventually, a delta can build so far out into the ocean that its gradient becomes too low to support the river's current; an event such as a flood can cause it to break a natural levee upstream, creating a new, steeper river channel that forms another delta.^[2],^[3] The abandoned delta eventually subsides.^[4]

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References:

1. Marshak, Stephen. (2001) Earth: Portrait of a Planet, New York: W.W. Norton & Company, ISBN 0-393-97423-5 pp. 528-9
2. Stanley, Steven M. (1999) Earth System History. New York: W.H. Freeman and Company, ISBN 0-7167-2882-6 p. 136
3. Marshak, pp. 528-9
4. Stanley, p. 136