Legend Of Triambakeshwar Temple
There are two legends associated with this place. One legend is about the origin of the place as Shiva's abode and the other is connected with the origin of river Godavari at the place.
Tryambaka - Lord Shiva's abode
The legend is very much same as one can find about the Lingodbhava murti of Shiva. Once Brahma and Vishnu were fighting for the highest place amongst the Gods. At the very moment a resplendent pillar emerged in front of them. They both decided to find either end of the pillar to prove their supreme position. Brahma took the form of a swan and went to search the upper end of the pillar and Vishnu taken a form of a boar went to search the lower end. Brahma came from the halfway and lied that he found the end of the pillar when Vishnu returned fruitless. Shiva who had emerged in the form of pillar or the linga, cursed Brahma for his lie that no one would ever worship him in the temple. Brahma gave Shiva a counter curse that he would be pushed in the earth in the linga form and he has to remain in that form at Sahyadri Mountain. Thus the three eyed one, in the linga form emerged at the eastern spur of Sahyadri ranges and made Tryambakeshvar as his abode.
Origin of river Godavari
The legendary account about this occurs in the Padma Purana. It states that sage Gautama was residing on Brahmagiri, the mountain behind Tryambakeshvar. His wife Ahalya had an earthern pot, which never remained empty. As such with the grains and the food obtained from the pot, the pious couple used to feed many hungry and needy people. Being jealous of this fact, the other sages decided to lessen the merit of Gautama. They sent a cow in his field and made it die as Gautama tried to drive her away with the Darbha grass. Gautama repenting on this started worshiping shiva. Shiva being pleased with his penance stood in front of him and gave him a boon. Gautama asked Shiva to release Ganga on earth at Brahmagiri to wash away the sin of killing the cow. Shiva did so and the River Godavari emerged from the place called Gangadwar on Brahmagiri.
This legend is so popular and effective that the local people call the river Ganga instead of Godavari.