- You may be looking for the star whale, an unrelated though similarly named species.
After an attempt by Nyssa to repair its chameleon circuit, the Fifth Doctor's TARDIS took on the form of a whale internally, externally, and personality-wise. The whale which had been the TARDIS dropped its passengers onto a beach and retreated into the ocean.
By projecting the Doctor's heartbeats into the ocean, he and Nyssa enticed the whale back to the surface so the Doctor could reestablish telepathic contact before the whale lost all memory of being the TARDIS. The Doctor restored the TARDIS to its familiar form and function. (AUDIO: The Deep)
The Sixth Doctor once said that he, possibly in an earlier incarnation, had seen a beached whale upon the sands at Ostend, Belgium. It lay dying for four days before its intestines exploded. Some of the human spectators died because of a disease in the rotting whale flesh. (AUDIO: Year of the Pig)
At some point before she visited San Francisco on 31 December 1999, Iris Wildthyme was in the city trying to find two humpbacked whales which she transported to the future in order to save Earth. (AUDIO: The Panda Invasion)