What causes the water in the blue currents to sink?

The water gets colder because cold, salty ocean water sinks to the bottom of the ocean basins below the less dense warmer water near the surface.

The difference of densities is what cause the sinking of the cold water.

Explanation:

The ocean encloses a certain water activity, creating the Global Conveyor Belt, which is about the thermohaline circulation, which is a system of currents.

The Global Conveyor Belt is crucial to maintain nutrients and carbon dioxide cycles. There we have warm water and cold water, each contain different percentage of salt and other minerals. Basically, the cold water tend to sink under the warm water which has more salt and more ability to absorb heat. This sinking of the cold water is due to the difference of densities, warm water is less dense that cold water, and according to physics, less dense fluids float over denser fluids.

So, basically the difference of densities is what cause the sinking of the cold water.