This book on the Physics of Waves by H. Georgi *([online PDF](http://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf))* provides some insight.

![](https://imagizer.imageshack.com/img923/528/DyLLf4.gif)

Incompressibility is an aspect of the ansatz I am using in generating the solution to Laplace's Tidal Equations (LTE) along the equator. If you think of the behavior as a liquid string that can't compress but can wiggle along its equatorial track, then this provides the closure necessary for the solution.

![](https://imagizer.imageshack.com/img922/8370/IKPfCA.gif)

![](https://imagizer.imageshack.com/img923/4687/aitHVq.gif)

The nature of a compressible liquid is that a displacement in one direction must be compensated by a displacement in another direction. This could be just a speed up in flow a la Bernoulli's principle.

https://youtu.be/UJ3-Zm1wbIQ

So the ansatz that I used in the following derivation is to apply a bending wiggle to the latitudinal displacement of the equatorial wave. This conserves matter by slightly displacing the position of the axis, pulled by gravitational/tidal forces -- at the expense of what would have to be a compensating change in the speed of the fluid.

![](https://imagizer.imageshack.com/img922/2638/PCuY7c.gif)

Without this ansatz in place, the latitudinal and longitudinal behaviors of LTE are uncoupled, yet we know they are physically coupled, otherwise the topological feature of the ENSO equatorial wave would not exist.