In fluid mechanics, the Taylor–Proudman theorem (after G. I. 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
That this is so may be seen by considering the Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, which are:
where
where
To derive this, one needs the vector identities
and
and
(because the curl of the gradient is always equal to zero). Note that
The vector form of the Taylor–Proudman theorem is perhaps better understood by expanding the dot product:
Now choose coordinates in which
if
Taylor Column
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.