According to the legend Gautam Rishi lived in this tapobhoomi along with this wife Ahilya. There was a small pond full of water and they gave water from the pond to all the other rishis, just enough only to suffice their urgent needs as there was scarcity of water. This led to jealousy among the rishis and they wanted to harm him.
So they performed a yagna asking Lord Ganesha to appear in form of a cow and die at the hands of the Gautam Rishi so that he is labelled as cow murderer. Though Lord Ganesha was not happy with this wish, the rishis were persistent. Finally he relented. And Lord Ganesha appeared in form of a sick cow in front of Gautam Rishi.
As soon as Gautam Rishi went to feed the cow, the cow died. With this the other rishis said that Gautam Rishi has committed a sin and the only way out it to do severe penance to Lord Shiva by asking for River Ganga to flow through his ashram to wash his sins. Gautam Rishi and his wife begin meditating.
After continuous meditation, Lord Shiva pleased with the penance visit the ashram along with Lord Brahma and Lord Vishnu to grant Gautam Rishi a boon. As a boon Gautam Rishi asks for River Ganga and secondly he pleads Lord Shiva to permanently reside in the place.The boon is granted and immediately river Ganges starts to flow through the ashram and this purifies Gautam Rishi. And Lord Shiva along with Lord Vishnu and Lord Brahma continue to reside in Tryambakeshwar in form of the three lingas.