>As far as an exact biennial (2-year) period, there may be something on the recent thread on tides: http://forum.azimuthproject.org/discussion/1480/tidal-records-and-enso/?Focus=12570#Comment_12570

You mean your comment with the period doubling? Yes eventually this could be some kind of a period doubling phenomena, the little peaks in between could belong to the smaller amplitude of a period doubling. I find it irritating though that the little peaks don't oscillate around a medium value (like in the logistic map) and that they seem to lead to a postponement of the higher peak, but then I haven't looked at many examples in dynamical systems which display period doubling. There may be examples which reflect this.

I didn't really understand what you where doing with the tidal, but then I got tired to check all the things there. In particular if Darwin is so close to Sydney (as someone said in the forum) then why should it take 3 months for the tide to arrive there?

>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

Well at least in
this diagram

it looks quite clearly (I find) as if the QBO index raises in odd years. This holds by the way also for the temperature (please add 58 to the year count):