I have to remember to search the Azimuth forum for previous discussions, such as the following pertaining to QBO
As far as an exact biennial (2-year) period, there may be something on the recent thread on tides:
The issue with an *exact* 2-year period is that it is hard to understand which year the peak of the oscillation starts -- in other words, whether it is an odd or even year, and vice versa for the valley. This is a symmetry argument and so the choice must be meta-stable. I am thinking that the yearly seasonal period doubles at some point in the past, and it gets locked into a groove. And then some unknown event would come along and perhaps force the system to skip a half a cycle and go from an odd year to an even year or vice versa.
This is similar to the magnetic polarity of the earth -- what decides the direction? And yet we know that the polarity does switch occasionally.