Does the water on the bottom of the ocean just stay on the bottom?

So if I put a glass of water out on a hot summer day, it would evaporate over time. But what i assume would happen is that the water molecules closest to the heat source (the top of the glass of water) would evaporate before any of the other water molecules

Assuming that is correct, there is water on the top level of the ocean that keeps getting evaporated and rained on over and over again. But also the water at the bottom of the ocean just stays down there cause it's not getting evaporated by the sun

Do I understand that correctly or am I missing something?