In fluid mechanics, the Taylor–Proudman theorem (after Geoffrey Ingram Taylor and Joseph Proudman) states that when a solid body[clarification needed] is moved slowly within a fluid that is steadily rotated with a high angular velocity
, the fluid velocity will be uniform along any line parallel to the axis of rotation.
must be large compared to the movement of the solid body in order to make the Coriolis force large compared to the acceleration terms.
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: where
The vector form of the Taylor–Proudman theorem is perhaps better understood by expanding the dot product: In coordinates for which
Thus, all three components of the velocity vector are uniform along any line parallel to the z-axis.
The Taylor column is an imaginary cylinder projected above and below a real cylinder that has been placed parallel to the rotation axis (anywhere in the flow, not necessarily in the center).
The flow will curve around the imaginary cylinders just like the real due to the Taylor–Proudman theorem, which states that the flow in a rotating, homogeneous, inviscid fluid are 2-dimensional in the plane orthogonal to the rotation axis and thus there is no variation in the flow along the
The Taylor column is a simplified, experimentally observed effect of what transpires in the Earth's atmospheres and oceans.
The result known as the Taylor-Proudman theorem was first derived by Sydney Samuel Hough (1870-1923), a mathematician at Cambridge University, in 1897.