Magnetic Taylor-Proudman Constraint Explains Flows into the Tangent Cylinder

Tangent cylinders (TCs) have shaped our understanding of planetary dynamos and liquid cores. The Taylor-Proudman constraint creates these imaginary surfaces because of planetary rotation, separating polar and equatorial regions, but cannot explain the flows meandering through them. Here, we establish and verify experimentally that magnetic fields aligned with rotation drive flows into TCs, linked to the flows along TCs by a magnetic Taylor-Proudman constraint. This constraint explains and quantifies how magnetic fields reshape rotating flows in planetary interiors and magnetorotating flows in general.