The Laplace tidal equations (derived from a linearization of the [primitive equations](https://en.wikipedia.org/wiki/Primitive_equations) describing fluid flow) provided the breakthrough which allowed ocean tides to be mathematically modeled. Not widely appreciated, but it's the horizontal gravitational force that causes the vertical displacement of these tides.

> "The actual imbalance force, called the tide-generating force (TGF) has horizontal components (called
tractive force) as well as the vertical component, and is distributed as shown below (this is a hypothetical case exaggerated to show the direction of TGF). Because it is difficult to generate vertical movement of water in the ocean, tractive forces are much more important for the generation of tides than the vertical component of TGF. That the moon’s gravity is stronger on one side of the earth than the other is crucial to the argument we just made. In fact, physicists generalize from this and call any deformational force that results from gravity varying from one point of an object to another “tidal”. "

![luanne](http://imageshack.com/a/img921/9549/jEqXWx.png)
from http://faculty.washington.edu/luanne/pages/ocean420/notes/TidesIntro.pdf

Yet practically speaking, the equations need to be tweaked quite a bit because ocean tides show significant spatial variability. The position of the moon in terms of the tropical or synodic month (27.322 days) plays a significant role as this establishes the longitudinal placement (Pacific, Atlantic, etc) of the strongest instantaneous tidal forces.

On the other hand, the QBO is almost completely longititudinally uniform. In this case, the draconic or nodal month (27.212 days) is the significant driver. This generates a horizontal or latitudinal forcing across the equator. So if the moon and sun are in max nodal excursions with respect to the equator, this will affect a change in the QBO direction, due to the cross-terms in the Laplace tidal equations:

![config](http://imageshack.com/a/img922/7527/zm7pUf.png)

I am not doing anything out of the ordinary, but simply placing a latitudinal-directed cyclic forcing in Laplace's equations and then reducing the set for a small angle approximation -- which I cover here:

http://contextearth.com/2016/07/04/alternate-simplification-of-qbo-from-laplaces-tidal-equations/

This is as solid a theory as I can devise from scratch and it matches the empirical observations of the QBO period precisely. In other words, if the nodal lunar month differed from 27.212 days by much more than a fraction of a percent, the entire theory would be invalidated (e.g. apply instead the tropical lunar month of 27.322 days and the empirical agreement is much worse).

Same goes for oceanic tides; if the period of the tides differed much from what is theoretically predicted by the lunisolar periods, the entire theory of a gravitational forcing leading to bulging tides would be invalidated.

So its essentially the same mechanism for oceanic tides applied to another fluid, leading to stratospheric tides.

The only problem is that you won't find this tidal derivation of QBO anywhere in the research literature. Do a [Google scholar search](https://scholar.google.com/scholar?q=%22quasi-biennial+oscillation%22+lunar+draconic&btnG=&hl=en&as_sdt=0%2C24) on QBO with the additional terms Draconic and lunar and you won't find much of anything. The scientific consensus is that the period of QBO arises as some sort of emergent phenomenon best described as an internal system resonance. Lindzen long ago considered lunar forcing and rejected the possibility, and so this is how the standard QBO model evolved.

In retrospect, where I think scientists such as Lindzen went wrong wrt QBO is in focusing on the QBO *velocity* and not the QBO *acceleration*. Acceleration is the operable characteristic, as that is what is observed in response to a Newtonian forcing in a non-viscous setting. And acceleration is what is formulated in Laplace's equations.