When they are not being fed, the five-kilogramme (11-pound) turtles pay little attention to their observers, straying away only when it comes time to lay their eggs on a nearby hillside.
But to disciples of saint Sultanul Arefin Hazrat Sultan Bayezid Bostami, who came to the Bangladeshi port city of Chittagong some 1,200 years ago, the turtles are fairies and genies considered to be incarnations of the holy man's followers.
Mohammad Khurshid Alam, head of the committee that looks after the site, said "These fairies and genies are carrying out some of the works of the saint to help the sick or those who need help in different ways, like getting married or even having good results in tests," he said.
One night recently, thousands of bare-foot men, women and children -- both Muslims and Hindus -- lit candles and burned incense at the grave of the saint, seeking divine blessing.
They turned to silent prayers as they tied strings on a plant growing from the grave, which is believed to have sprung from a stick the saint carried.
Alam said people from across the world had come to the shrine to follow the rites -- the last of which is to feed the "spiritual turtles" in the pond.
Bread and bananas are the favourite food of the turtles, which pop up from the water at feeding time.
Some devotees even clean the shells of the turtles and then use the water to wash themselves or the sick.
Caressing and cleaning one turtle, Ferdousi Begum said she came to the shrine because her son suffers from rheumatism.
"They are fairies and genies, and I believe washing my son with the water will heal his illness," she said.
Others said they had already been healed by the ritual.
"A blind man came and as he left after completing the whole ritual, including washing his eyes with the water, he got back his sight," said Alam.
"People would not come here again and again unless they got results, especially those appearing for tough school tests," he said.
Legend has it that Bayezid Bostami had prayed to God before his death that the turtles would be fed by the people who came to the shrine.
But there are some on the 15-member committee overseeing the shrine who are not even sure that Bayezid Bostami's mortal remains are buried at the site, with some saying he was interred back in Iran.