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canyon a narrow chasm with steep walls, cut into the earth by water
gorge A deep, narrow passage with steep rocky sides; to stuff with food
ravine a deep, narrow valley in the earth's surface worn by running water

Examples  

The Grand Canyon was carved by eons of water erosion from the Colorado River.
A flash flood races through the ravine at least once a year.
The gorge of the Rio Grand is deep near Taos, New Mexico.1
The children gorged on blueberries they found in the woods.
Notes1
canyon would name the largest, deepest of the above geological features. See arroyo/gulch