The same phenomenon occurs in planetary atmospheres; this rotating tank is basically a mini-version of our the atmosphere. Where there are obstacles — like mountains, air has an easier time flowing around the mountain instead of over it
The Taylor column, illustrating the Taylor-Proudman theorem in a rapidly rotating fluid
After breaking free, world's largest iceberg is stuck spinning in circles
1Ghil, M., Simonnet, E. (2020). Geophysical Fluid Dynamics, Nonautonomous Dynamical Systems, and the Climate Sciences.
2Nicole Sharp - August 21, 2024. Trapped in a Taylor Column.
3\(\frac{\partial u}{\partial z}
= \frac{\partial v}{\partial z}
= \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}
= 0 \Rightarrow \frac{\partial u}{\partial x}
+ \frac{\partial v}{\partial y}
+ \frac{\partial w}{\partial z}
= 0 \Rightarrow \frac{\partial w}{\partial z} = 0
\Rightarrow (2\boldsymbol{\Omega} \cdot \nabla)\mathbf{u} = 0\)
This constraint is called the Taylor-Proudman theorem. In this case all three components of the relative velocity are independent of the direction parallel to the rotation axis.
if \(w\) is zero at some level, for example at a rigid, horizontal surface, it remains zero for all \(z\). The motion is then completely two dimensional and can be pictured as moving in columns, each column oriented parallel to the rotation axis and moving so as to maintain this orientation. The columns themselves are most often referred to as Taylor columns.