Inertial oscillation
In a rotating system, when a particle trapped in the horizontal plane is not acted on by any external forces, it will move in a circular motion. This is called inertial oscillation. Put differently, inertial oscillation in a rotating system is just as natural (or obvious) as straight motion at uniform velocity in a stationary system.
When sea water and the atmosphere carry out inertial oscillation, a wide area of fluid moves in the same phase, and each section of the fluid maintains a relative positional relationship with the other sections of the fluid. If a boat on the sea inertially oscillates, unless there is an island nearby, the people on the boat would not realize they were oscillating inertially.
Based on a solution to the formula for inertial oscillation, it is possible for a sections of a fluid to revolve around each other. However, in the atmosphere, this would kind of current would revolve like a high atmospheric pressure system, but with no pressure gradient, because Coriolis' force and centrifugal force are in balance. If a current like this occurred at the North Pole, looking from outside the earth you would see a mind-blowing current that was moving at the same speed at the rotation of the earth but in the opposite direction. It is highly unlikely that a current like this will ever occur on a large scale in the atmosphere or the oceans.
