Jim, Appreciate the interest as always.

I'm trying to relate the LTE modulation factor to something akin to a Reynolds number (Re) or a Richardson number (Ri), which makes it a single scalar that describes the breaking or folding of the waves (like a turbulence factor but not chaotic) and to the primary wavenumber.

Right now the trend of the LTE value is closer to zero if the climate index is measured close to the equator (QBO is the lowest) and it tends to increase as the index moves away from the equator. The ordering is about like this:

QBO < ENSO < (AMO ~ IOD) < PDO < ( NAO ~ AO ~ SAM ~ PNA)

The wavenumber of QBO approaches zero because the standing wave encircles the equator and cycles in unison. Correspondingly the wavenumber values may be required to increase away from the equator -- which is forced to be smaller closer to the poles -- but it also may be due to the specific waveguide bounding box of the index. For example, the equatorial Pacific is widest and thus ENSO has the lowest primary wavenumber next to QBO.

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Added for entertainment. This is a typical YouTube search for "fluid motion in glycerine"

https://youtu.be/Yy0-1nWVgls

Notice how the fluid flow is complete reversible in the sense that all the dispersion observed "undisperses" on reversing direction. This is a consequence of the low Reynolds number limit -- via the highly viscous glycerine media -- of the Navier-Stokes equation.