You provided a good reference above showing the increasing utility of analog QM to atmospheric geophysics.
Quasi-particles are collective excitations of any sort in Condensed Matter to which a Particle analogy is applied. Newton's Point-Mass Assumption for planetary objects is a prototypical case.
Since [Tamm 1938], a defined class of collective excitation are Phonons; Quanta of acoustic and mechanical energy. Under modern Quantum Field Theory, all QM fields are fluid ("hydrodynamic"). Many kinds of waves, jets, and vortices are effectively classed as Phonons. Collective mechanical atmospheric motions are Phonons.
Generally in chaotic geophysics we consider seething Phonon Wave Packets, with sub-waves continuously created and annihilated within an "envelope". Thus ENSO is not one quasi-particle, but a sequence of Phonons created and annihilated in its bounds. We can identify the periodic appearance of the vast warm water mass in the Western Pacific as a primary Phonon involved.
Chladni Plate vibrations are a good starting model for specific atmospheric effects, like coherent geometric patterns seen at Saturn's Poles. Oobleck Physics take oscillatory driving into Chaos, the suggestion being that periodic forcing creates hard to predict outcomes in a complex space-
QBO wave-number is properly two non-zero angular wavenumbers (for easterly and westerly motions, respectively) relative to Earth Frame. Precession, terrain, Coriolis, sunspot cycles, ENSO, and other variables, cause calculable QBO wavenumber variation.
AO and AAO most closely approximate wavenumber zero, as zonal (symmetric) flows.