I think the phase flip and biennial mode go hand-in-hand. I have noticed a recent spate of papers on the biennial mode of ENSO. Here is a very recent one by NASA Godard scientists:
> Achuthavarier, Deepthi, Siegfried D. Schubert, and Yury V. Vikhliaev. "North Pacific decadal variability: insights from a biennial ENSO environment." Climate Dynamics (2016): 1-19.
The above excerpt is the typical explanation via a wordy rationale of how a succeeding year is prevented by the previous year from cycling, thus creating a biennial period.
Which differs from the purely mathematical explanation of a Mathieu sloshing formulation showing an inherent period doubling (or frequency halving), such as described here by a group at CNRS in France:
> Rajchenbach, Jean, and Didier Clamond. "Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited." Journal of Fluid Mechanics 777 (2015): R2.
What I have been doing is noting the empirical observations from the climate scientists and then tying that into the math that the physicists and engineers have been developing for other hydrodynamics applications. What's interesting is that these research efforts are concurrently advancing and the timing is perfect to tie the hydrodynamics concepts to the biennial ENSO concept.