The key to analytically solving Laplace's tidal equations (Navier-Stokes) along the equator is to use the ansatz of a non-fixed equator. Solved [here](http://contextearth.com/compact-qbo-derivation/)

This is the rationale:
![](https://pbs.twimg.com/media/DmBMhDQX0AAH-5s.jpg)
from "A Chorus of the Winds—On Saturn!" P. L. Read
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018JE005625