A simulation that captures both the QBO and the transition from the Semi-Annual Oscillations 
One can see how the semi-annual oscillations bleed into the QBO, with the ripple barely visible at 20 hPa, but still there. My bet is that a useful first-order model is either a modulation of the wave equation, ala Mathieu, or of a RHS forcing from a semi-annual cycle. Or it could be some of both. A similar contour plot would not be hard to duplicate as a continuous transition, coded in Mathematica.
Part of the reason for doing this is to come up with first-order parameterizations that don't require the complexity of a GCM. If the QBO is strongly associated with ENSO, this might be a useful approximation.
The strange box-like artifacts observed at 40 hPa in #17 are not seen in this simulation. That one is still a mystery. It is very tempting to pursue that behavior but if it turns out to be a data transformation artifact, that would be wasted time.
S. Schirber, E. Manzini, and M. J. Alexander, “A convection‐based gravity wave parameterization in a general circulation model: Implementation and improvements on the QBO,” Journal of Advances in Modeling Earth Systems, vol. 6, no. 1, pp. 264–279, 2014.