The book of Joshua stages the entry into the land as a second Exodus. The priests carrying the ark step into the water, the flow stops upstream, the people pass over on dry ground, and twelve stones are taken from the riverbed and set up at Gilgal so that children would ask what they meant. The river is thereafter the eastern edge of the promised land, and the point where a people stopped wandering.
Rachel Havrelock's study takes that boundary as its subject and shows how unstable it is. Two and a half tribes settle on the eastern bank and have to be argued back into Israel; Judges 12 has the men of Gilead killing fugitives at the fords by making them pronounce the word shibboleth; Ezekiel and Numbers draw the border differently; and the river's function as a line, rather than any quality of the water, is what the texts keep returning to.
The prophetic cycle attaches to it too. Elijah strikes the water with his rolled cloak and crosses dry, and is taken up on the far side; Elisha strikes it and crosses back, inheriting the office. The Syrian general Naaman is told by Elisha to wash seven times in the Jordan to be cured of his skin disease, is insulted by the smallness of the river compared with those of Damascus, and is healed when he does it anyway, a story about the ordinariness of the means that later Christian writers used constantly.