The Taylor-Proudman Theorem says when a solid body is moved slowly within a fluid that is steadily rotating at high angular velocity, that the fluid velocity is uniform along any line parallel to the axis of rotation.
A consequence is that an object at one level in the rotating fluid will cause the fluid to flow around a virtual object projecting it to all levels. In an Atmosphere, this might be flow around an object at ground level affecting the flow above the object as if the object were taller. This is called a Taylor Column.
This has been incorporated into an argument that Jupiter's Red Spot is shallow because if it were deep, it would project a complimentary red spot in the other hemisphere.