Typically most species of turtles by nature are nocturnal. However some have been known to become diurnal once kept in captivity. They may begin to start resembling a routine similar to their owners and be more active during the day since all of the noise etc. disturbs their sleep and may leave them a bit confused when they have been trying to sleep during the day like they’ve been accustomed to most of their lives.
One of the main reasons turtles are naturally nocturnal creatures is to reduce the risk of predation to themselves or their offspring. In nature some species such as the green turtle have been known to sometimes exhibit both nocturnal and diurnal behavior.
Tortoises and terrapins usually sleep with their eyes closed. They would also prefer to sleep in a shelter such as underneath a piece of driftwood. However others have been known to just pass out asleep wherever they may be at the time. A few have been known to sleep literally latching themselves in between rocks.