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This is an earthlike planet in every respect (same 24 hour day, same orbital year, etc) except it is an ocean world. There are no continents, and the global ocean is significantly deeper (10 miles, or deep to the point the topography of the ocean floor would have little role in the shape of the currents.) I assume the main factors here would be tidal forces of the sun/moon, the Coriolis effect, maybe sun exposure and wind currents, and the formation of ice caps at the poles.

I've poked around quite a bit and found a textbook covering surface gyres that states "wind-driven surface currents only affect the top 100-200m of water, which I would assume would mean these currents move with the circulation of the planet's atmospheric cells and jetstreams.

What I would like to know is what the deep-sea currents of this ocean world would look like. Would they emulate the currents of the atmosphere?

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If you have any topography on the ocean floor, it will strongly affect the cold ocean currents. Simply because the cold currents do NOT flow "in" the ocean but rather "over" the ocean floor, as if they are pretending to be giant rivers.

The warm ocean currents flow along the surface, and would ignore the bottom topography, if deep enough. They might even cross over or flow in opposite direction to underlying cold currents, if the water is deep enough. For a world with no shores or shallows, these warm currents would very much resemble the winds above them. i.e. alternating bands of "jet streams" with rotating regions inbetween.

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    $\begingroup$ Came here to say this, at least the part about the alternating bands of currents. I’m no expert, but my guess is that the surface currents would resemble the jet streams on a gas giant like jupiter, which move in opposite directions and stir up storms (rotating regions) in between them. $\endgroup$ – HolocronCollector Oct 23 '20 at 2:02

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