An "extra" dimension helps to show what happens when the solution to Laplace's Tidal Equations along the equator develops greater modulation -- equivalent to wave breaking wrapping around a torus.

![](https://imagizer.imageshack.com/img922/9703/V7RV2c.png)

The wave can curl in the left or right hand sense, but since it's topologically confined along the equator there's no preference in the direction. The lack of chirality allows the two curls to cancel and left with the z-projection.

https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch12