Taylor–Proudman theorem

In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity ${\displaystyle \Omega }$, the fluid velocity will be uniform along any line parallel to the axis of rotation. ${\displaystyle \Omega }$ must be large compared to the movement of the solid body in order to make the Coriolis force large compared to the acceleration terms.

The Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, are

where ${\displaystyle {\mathbf {u} }}$ is the fluid velocity, ${\displaystyle \rho }$ is the fluid density, and ${\displaystyle p}$ the pressure. If we assume that ${\displaystyle F=\nabla \Phi =-2\rho \mathbf {\Omega } \times {\mathbf {u} }}$ is a scalar potential and the advective term on the left may be neglected (reasonable if the Rossby number is much less than unity) and that the flow is incompressible (density is constant), the equations become:

...
Wikipedia