This will be a short note, because it is intrinsically so.
The Coriolis effect is observed between two Newtonian objects or bodies, one of which is in a rotating frame of reference. Independent objects can move individually without any physical connection to the other.
The Earth’s atmosphere, oceans, mantle, outer core and inner core are not Newtonian objects because none is a separate independent body or object.
They are all parts of the same Newtonian object, the Earth. All are also in the same rotating reference frame.
Therefore any circular motion observed in the atmosphere and oceans are not due to the Coriolis Effect, but due to an external forcing such as the conduction of plasma Birkeland currents between the Earth’s surface and the ionosphere.