Taylor-Proudman theorem

His model was based on another well-known feature of fluid mechanics, the Taylor-Proudman theorem.

If the curl of this equation is taken, the result is the Taylor-Proudman theorem:

The vector form of the Taylor-Proudman theorem is perhaps better understood by expanding the dot product:

Neglecting friction and vertical motion, as justified by the Taylor-Proudman theorem, we have:

Here the fluid is subject to the Taylor-Proudman theorem which says that small motions will tend to produce purely two-dimensional perturbations to the overall rotational flow.

The phenomenon is explained via the Taylor-Proudman theorem, and it has been investigated by Taylor, Grace, Stewartson, and Maxworthy - among others.

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 , the fluid velocity will be uniform along any line parallel to the axis of rotation.

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, homogenous, inviscid fluid are 2-dimensional in the plane orthogonal to the rotation axis and thus there is no variation in the flow along the axis, often taken to be the axis.