The sons of Sagara went looking for their father's horse and found it grazing beside the meditating sage Kapila. They called him a thief; he opened his eyes and there were sixty thousand heaps of ash. Their souls could not rise until the river of heaven touched them, and for generations nobody could bring her down. Bhagiratha gave up his kingdom and stood in penance until Brahma agreed to release Ganga. But a river falling from the sky would split the earth open, and Bhagiratha went on standing until Shiva agreed to take the blow. Ganga fell, proud, meaning to sweep the god away, and vanished into the coils of his hair. She wandered there for years. When Bhagiratha asked again, Shiva let her out in a few streams. One of them washed over the sage Jahnu's hermitage; the angry sage drank the whole river and, on being begged, let her flow out of his ear, which is why she is Jahnavi. Bhagiratha walked ahead of her in his chariot to the sea, and where the water reached the ashes the sons of Sagara went up to heaven. The river is Bhagirathi for the king, and Shiva is Gangadhara, the one who bears Ganga.
The Skanda Purana's early mention of Kedarnath, from around the seventh or eighth century, comes inside a telling of the Ganga's origin; the Himalayan shrine and the river's descent are tied together there.
What is different here:
Localises the descent to the Kedar region; the earliest textual anchor for the temple.
The Bhagavata keeps Bhagiratha's penance and Shiva's hair but changes where the river begins: when Vamana's foot went through the top of the cosmic shell, the water of the outer ocean came in through the crack and washed the foot of Vishnu, which is why she is called Vishnupadi, the one from Vishnu's foot, before she is ever Ganga of the earth.
What is different here:
Ganga originates at Vishnu's foot, so the descent is from Vishnu's realm through Shiva's hair.
At Elephanta the moment is carved with Shiva and Parvati standing side by side as the three-headed river comes down into his hair, Parvati turning slightly away: the sculptors caught the co-wife's arrival as well as the rescue of the earth.
What is different here:
Iconographic: Parvati's displeasure at Ganga's arrival is read into the pose.