I created a QBO page that is a concise derivation of the theory behind the oscillations:
http://contextEarth.com/compact-qbo-derivation/
Four key observations allow this derivation to work
- Coriolis effect cancels at the equator and use a small angle (in latitude) approximation to capture any differential effect.
- Identification of wind acceleration and not wind speed as the measure of QBO.
- Associating a latitudinal displacement with a tidal elevation via a partial derivative expansion to eliminate an otherwise indeterminate parameter.
- Applying a seasonal aliasing to the lunar tractive forces which ends up perfectly matching the observed QBO period.
These are obscure premises but all are necessary to derive the equations and match to the observations.
This model should have been derived long ago .... that's what has me stumped. Years ago I spent hours working on transport equations for semiconductor devices so have a good feel for how to handle these kinds of DiffEq's. You literally had to do this otherwise you would never develop the intuition on how a transistor or some other device works. The QBO for some reason reminds me quite a bit of solving the Hall effect. And of course it has geometric resemblance to the physics behind an electric motor or generator. Maybe I am just using a different lens in solving these kinds of problems.
Paul,
More fascinating work.
Unfortunately, I have little time to keep up with developments, but I notice there has been a kerfuffle over an "unexpected" disruption to the QBO in Feb 2016.
See http://science.sciencemag.org/content/353/6306/1424
Can your work throw any light on this?
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Thanks Bill. I put a new post up on that question.
Nobel Prize in physics on this topic: https://johncarlosbaez.wordpress.com/2016/10/07/kosterlitz-thouless-transition/
These curl equations are fascinating and are of course endemic in applications from electromagnetics to fluid dynamics. As a well-known example, the vortices that spin off in latitude from the longitudinal equatorial flow lead to hurricanes. Visualize in terms of the GIF from Brian Skinner above -- the equivalent of the equator runs along the diagonal in this case. Notice that right along the diagonal, the arrows point only in one of two directions -- the equivalent of east and west.
The problem is that the math gets complicated quickly as so much remains underdetermined. It seems that the equator is at a perfect position for a metastable vortex/antivortex pair, in that the Coriolis forces exactly cancel and which direction the winds blow right along the equator is very sensitive to forcing.
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