Short period => long period, all done and substantiated
> *[left] Fig. 6.(a) Diagram illustrating the process of wavefiltering that causes the non-linear interaction between QBO and AO/SAO to produce multi-year beat periods.*
Below demonstrates how the beat periods are produced -- direct forcing feed-through, with possibly some natural band-pass filtering or resonance.
Geophysicists should have figured this out already 50 to 100 years ago, considering how obvious it is in retrospect to apply plain old Newtonian forcing via the even more obvious long-period tidal factors that have been known for an eternity.