How do ocean currents work on a tidally locked planet?

Question

I am currently designing a tidally locked world with a big enough ocean to transfer heat from the day side to the night side and vice versa. Here is a map of my world:

The darker sides are supposed to be the dark side of the planet, while the brighter area is the day side, with the center being directly facing its parent star.

I'm trying to figure out how the ice caps in the dark side would grow in order to add them in my map, and for that I feel like I need some information about the planet's ocean current's. Assuming the planet rotates from left to right, what directions would the currents of my world take?

If the planet is tidally locked, it won't 'rotate' at all relative to its sun. — Monty Wild, Jan 20 '24 at 09:18
What do you mean? Doesn't tidally-locked mean that the time it takes for a planet to rotate around its axis is the same as the time it takes to complete one orbit around its parent star? Or am I missing something? — ΓΙΑΝΝΗΣ ΜΙΧΑΗΛΙΔΗΣ, Jan 20 '24 at 09:32
I mean that there won't be any relative rotation on this world as in earth-sun, or earth-moon from the point of view of earth. The sun will always be in the same position, and the water will always bepulled in the same direction. Any circulation will be thermal or caused by libration. — Monty Wild, Jan 20 '24 at 10:17
Does this answer your question? How would the ocean currents of a tidally locked super-Earth work? (Also, for reference see this answer and know that currents are quite similar to wind.) — JBH, Jan 20 '24 at 17:10

Escaped dental patient. · Answer 1 · 2024-01-20T10:38:30.723

By far the greatest forces your atmosphere and water are going to be moved by are thermal.

Things like the Coriolis force driving differential circulation (and various turbulent competing cells) in the different hemispheres will be negligible, the same with trade-winds.

You would get a permanent thermal rise at the centre of the map, the point where the star is overhead. This (or these, there's no reason it won't split just like at Jupiter's North pole, but less stable) will tend to rotate and produce rotating winds, but the direction, hardly affected by the Coriolis effect will be quite unstable - both in direction and they'll wander around.

Between the centre and the twilight-zone, the prevailing wind at ground level would be towards the centre, in the higher atmosphere, it would be away from the centre. Picture a big rolling doughnut of a light-side vortex.

Around the rim, the twilight-zone, there would be turbulence and instability where the cold-air meets the high-up hot air from the light-side. There would be downward-streaming air currents in swirling vortices - and just as at the midday point, they would be unstable and mobile. On perhaps an hourly basis, the temperature might vary by many tens of degrees Celsius.

Needless to say perhaps, the moisture will be carried away from the heated areas to the cold areas. I imagine a frozen ridge of precipitated snow over packed-ice, several kilometres high ranging several hundred kilometres past the twilight-zone. There would be continuous melt-water producing lakes and rivers flowing towards the light-side - inevitably evaporating before reaching a "Sea". Desiccated salt-pans would form in depressions over much of what might once have been oceans

How do ocean currents work on a tidally locked planet?

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