Kâlindî was the daughter of Sûrya, the sun god. She was blessed to become a sacred river, also known as the Yamunâ. It flowed from the Kalinda mountain and entered the Gangâ at Prayâga, a very sacred confluence.
At the birth of Krishna, his father Vasudeva had to switch the infants of his two wives. He had to cross a flooding Kâlindî River. The goddess of the river miraculously helped him cross back and forth with the babies. There is a strange story in the Bhâgavata (Skandha Ten) about Balabhadra Râma, Krishna’s brother and a divine incarnation in some lists, and the Kâlindî.
Balabhadra Râma had had a little too much liquor to drink and was playing with the cowherd girls (gopis). He wanted to swim with them so he had to pull the Kâlindî over to them with his plough. The Bhâgavata Purâna stated that Krishna and Arjuna were walking together along the Kâlindî and saw a beautiful woman, who turned out to be Kâlindî herself, practicing austerities (tapas).
Arjuna learned that she was doing these in order to gain Krishna as her husband. When Arjuna told Krishna, Krishna took the goddess Kâlindî in his chariot to Dvârakâ and married her. Krishna and Kâlindî had ten sons. There was a story in Vâmana Purâna saying that Kâma-deva (the god of love) shot some of his love arrows at S´iva, when S´iva was very depressed over the death of Satî.
S´iva became so excited that he jumped into the river Kâlindî—and that is why its water is black. In Agni Purâna the goddess Kâlindî was depicted as black in color and riding on a tortoise, carrying a water pitcher in her hand. According to Padma Purâna the river Kâlindî was so holy that to drink her water or bathe in her divine flow would purify anyone from their sins and give them the merit (punya) to gain heaven (svarga).