The link you provided is a great tool but makes it hard to grasp the actual flow of the oceans, there is too much going on at the same time.
This one might be easier to understand while still very detailed:
https://en.wikipedia.org/wiki/File:O...rderless)3.png
Other than that, the wikipedia page has other interesting maps :
https://en.wikipedia.org/wiki/Ocean_current
Fluid dynamic is complicated, you don't have to dig too deep to get a plausible world.
ONImap currents from hell.png
Some things to note:
The equatorial currents, it's a mess and actually do not have a big impact on climates since they travel at a constant latitude. The counter current is the weakest and only exist because of the friction from the 2 other parallel currents.
A lot of the current also flow between the islands.
I added polar currents. they flow opposite to the westerlies in the high latitudes. On Earth they only exist in the Beaufort sea and somewhat around Antarctica.
I added some white currents. Some currents aren't really cold or hot nut I haven't spent a lot of thoughts on the temperature of the currents.
Other things:
I think Jean-Abel meant that the north pole is missing a bit of land. You need to have a small strip of land at the edge, or it could be water.
But right now the north pole is made of water and land at the same time. That is not possible.