In a tidally-locked planet that rotates about a barycentric point that’s located outside of its own sphere, what would the coriolis forces be like? What would the circulation patterns look like, how similar or different might they be from those of Earth’s?
This needs to consider not only the direction of the centrifugal force, but those of the moving fluids (air, water weather patterns and mantle convection) as they move away from the sub-barycenter point to the half way great circle, and then converge again as they approach the antipode.
The coordinate systems refers to the sub-barycenter point as being one pole, and its antipode is the point opposite the sub-barycenter; the planet doesn’t have a rotation axis.
Something like winds and weather patterns driven by coriolis forces will expand over the surface of the planet until they reach the half-way mark where they will have expanded to their maximum size. This is also the half-way mark of a great circle (the shortest distance between two points on the surface of a sphere). Thereafter they will converge once more on their approach to the other, opposite pole, the antipode.