Symbolism, Imagery, Allegory
Are you a mythological figure who enjoys being alive? A word of advice: you might want to avoid rivers. Don't say we didn't warn you.
With their constantly flowing, ever-changing waters, rivers are the perfect symbol for transition. In fact, they usually represent the biggest transition of all: the change from life to death. This is laid out pretty clearly with the River Styx, the river that all mortals must cross before entering the deathly Underworld.
Rivers pop up a lot in the Orpheus and Eurydice myth, which makes sense, since there's a lot of traveling to and from the Underworld in this story. Eurydice is next to a river when she dies from her snake bite, and then, when Orpheus goes to find her, he must cross the River Styx. Later, when Orpheus tries to cross the River Styx for a second time (after losing Eurydice again), the Ferryman denies him access, blocking him from transitioning to the afterlife again. Finally, when the Maenads kill Orpheus, they throw his beautiful head into a river.
So yeah, a lot of "death and river" imagery in this story. In fact, if the myth of Orpheus and Eurydice were a movie, we might nominate "rivers" for a Best Supporting Actor Oscar.
Don't think this is just a bunch of old stuff, though. Rivers appear as symbols for death and transition in more modern works of literature, too. Check out our thoughts on rivers in The Giver and The Mill on the Floss for just a couple of examples.