The white stuff is a fungus that is growing on the shell...this is usually caused from bacteria growing in the water, the best way to deal with this is frequent water changes and once a week plus vacuum the aquarium out,a good strong filter helps, and to rid of this, you can put a sulfa block turtle from pet store in tank, and make sure he is getting out on the basking spot where it is up 80's in temperature frequently in a day as he needs his shell to dry off, this will also prevent this problem, hopefully this will help get rid of the fungus over time... Sincerely, Susan