A view of rising seas from the MarAzul
I use the follow current charts which I have modified to navigation charts so I may reference my boat's position relative to the currents and the project course relative to the currents at any given time.
These ocean current are generated partially from the earth turning daily on it's axis, the effects of which are known as the Coriolis effect. The other major power source of this world wide current flow is the introduction of the cold water into the oceans from Rivers and streams, often very cold water from glacier melt. This cold water displaces the warmer sea water adding to the flow to the ocean currents, especially the Kuro Siwo current in the North Pacific and the Gulf Stream in the North Atlantic.
How long these currents will continue to be powered is no-doubt a function of how long with the Glaciers feed the cold water into the ocieans. Since we know, Glaciers are predicted to be gone, especial those that exist between the 30 latitudes North and South, before the end of this Century, perhaps closer to 40 - 50 years. Farming in these area watered by glacier melt will really become a challenge. But without the water injection into the Sea, the sea level rise reaches it's maximum, and these major Ocean current probably cease to flow as we know them to through out human history.
Without these current, you can suspect the land warmed by the currents, Canada, Northern United States, and Northern Europe become one hell of a lot colder. Probably triggering a new Ice age in the Northern Hemisphere. At that point the sea levels begin to slowly recede for several thousand years until it drops some 190 feet from todays level as the water is transfered once again to a Glacier Ice Pack.
I do hope our grand children can learn to deal with the events. I seriously doubt they will find one among them that can devise a plan to stop the cycle. No doubt something will, but I wouldn't bet on it being man made. I expect the first thing that we will be forced to deal with beyond a little flooding in Miami and New York, is lack of water for farming in the most populated areas on earth. It should be anticipated now! But it isn't!