This little green turtle has been particularly friendly of late. These were taken last week but we saw her again today.
Turtles can be approached exceptionally closely if they allow it. They will flee at speed if you chase them however. The best thing to do when you encounter a turtle in the water is to hold your position and watch for a while before moving in closer when they ge used to you. Never hover above a turtle however as they really don't feel comfortable with this and will flee.
Of course if they feel comfortable they may well maneuver themselves under you so don't freak out if it happens. Just go with the flow and the mellow little dude's will do the same.