>"Anyways I give up trying to understand your calculations."
As it turns out, the other component in QBO is what they call a Semi-Annual Oscillation (SAO)
[The theory of the QBO](http://www.ugamp.nerc.ac.uk/hot/ajh/qbo.htm)
"Holton and Lindzen (1972) were the first to propose a model of the QBO based on vertically propagating waves. Originally it was thought that the Semi Annual Oscillation (SAO) in the upper stratosphere played an important role in the QBO. More recently they showed that while the SAO was important, it was not necessary for the formation of the QBO.The mechanism was further explained by Plumb (1977) who showed that the maximum acceleration occurs just below the maximum phase speed, leading to descent of the maximum with time. "
"Fig 1. The monthly zonal mean wind in m/s against pressure in mb as seen the the UKMO assimilated dataset at 1.25 ° north of the equator. Easterlies are coloured yellow to blue and westerlies orange to red. The zero line is in thick black and every 5m/s is delineated in thin black. The QBO is roughly between 10mb and 100mb in height extent. Above 3mb the Semi-Annual Oscillation (SAO), a harmonic of the seasonal cycle can be seen, being westerly near the equinox and easterly near the solstice."*
See the clear semiannual oscillation above the biennial oscillation? This Mathieu model fit may be a direct clue that the semiannual=biannual variation at altitudes higher than (in the mesopshere) the QBO modulation influences the formation of the biennial cycles below (in the stratosphere).
It may also refute what Lindzen found. If it wasn't for the strong biannual/semiannual modulation ala the Mathieu DiffEq, then the generated oscillation would likely have a completely different characteristic.
This is a more recent description
V. S. Babu and G. Ramkumar, “Planetary waves–major forcing agent in generating stratospheric and mesospheric quasi biennial oscillation,” CURRENT SCIENCE, vol. 106, no. 9, p. 1260, 2014.
Amazing what machine learning and search optimization can find!