Simulation of the Great Ocean Conveyor by CFD?

Woods Hole Oceanographic Institution reports that the Great Ocean Conveyor's "Pump" Switches Back On.

The “pump” in question is in the western North Atlantic Ocean, where pools of cold, dense water form in winter and sink beneath less-dense warmer waters. The sinking water feeds into the lower limb of a global system of currents of the Great Ocean Conveyor. To replace the down-flowing water, warm surface waters from the tropics are pulled northward along the Conveyor’s upper limb.

What will be the future of the Conveyor under different scenarios of global warming? In principle we should be able to get the answer by Computational Fluid Dynamics CFD, but what is state-of-the-art of CFD? Can you simulate the Conveyor by CFD, today or in 50 years? Compare with Global Climate Modeling.