【go below】 —(Nautical) go to the lower (underwater) levels in a ship:

• Nora and I went below to our bunks to make our beds and settle in before the ship left the channel.

【go under】 —

1. (of a person or ship) 【go below】 the surface of the sea:

• Our boat went under in no time at all. Some time later the submarine approached us, spraying machine gun tracer bullets….

2. (of a business) fail:

• A few weeks before the company went under he checked to see if his pension was safe.

3. lose consciousness under the action of anesthesia, etc.:

• No one trained in administering anesthesia was dedicated to that task alone in his operating room as she went under.

See also: come down / go down.