### Taylor-Proudman theorem

(theorem regarding movement through a rotating fluid)

The **Taylor-Proudman theorem** says when a solid body is moved (at
most) slowly within a fluid that is steadily rotating at a high
angular velocity (relative to the solid body's motion, if any),
that the fluid velocity is uniform along any line parallel to the
axis of rotation. If the solid body is cylindrical (unvarying
shape) through the height of the rotating fluid (presuming the fluid
is rotating around a vertical axis), this result is intuitive, but
if the body is "shorter" than the height of the rotating fluid, the
fluid not only flows around the object but flows as if the object
were the full height of the rotation, i.e., around a virtual object
projecting it to all levels, a far less intuitive phenomenon. In
the atmosphere of a rotating planet, this could be flow
around an object at ground level affecting the flow above the object
as if the object were taller. This vertical region of fluid-rotation
is called a **Taylor column**. The phenomenon is explained through
the mathematics of fluid dynamics, and is confirmed by fairly simple
experiment. This theorem has been used in an argument that
Jupiter's **Red Spot** must be shallow because if it were deep,
it would project a complementary red spot in the other hemisphere.

(*fluid dynamics,rotation*)
**Further reading:**

https://en.wikipedia.org/wiki/Taylor-Proudman_theorem

https://en.wikipedia.org/wiki/Taylor_column

https://www.usna.edu/Users/oceano/barrett/SO414/Lesson9.pdf

https://www2.atmos.umd.edu/~nigam/Hoskins-James.pgs.61-64.pdf

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