Editing Appendix/Ramblings/ToHadleyAndImamura (section)

====Various Thoughts====

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<li>In the Blaes85 model, the "constant phase locus" swings through a total angle of,
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<math>~m\Delta</math>
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<math>~=</math>
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<math>~2\tan^{-1}\biggl[ \frac{\mathcal{A}}{\mathcal{B}} \biggr]_{\eta=1} + \pi \, .</math>
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For example, in the model displayed, above, <math>~[\mathcal{A}/\mathcal{B}]_{\eta=1} = 0.4583</math>.  Hence, <math>~2\Delta = 4.001</math> radians.</li>

<li>
We need to resolve the apparent discrepancy between the value of the leading constant that appears in the GGN86 eigenfunction versus the one that is found in the Blaes85 eigenfunction (when evaluated for <math>~n=0</math>).  Graphically, the Blaes85 amplitude function appears to make more sense, but a physically based explanation needs to be identified.
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<li>
The amplitude and phase functions obtained from the Blaes85 work appear to match &#8212; qualitatively, if not quantitatively &#8212; the amplitude and phase functions published by the Imamura &amp; Hadley collaboration if we subtract the leading "unity" constant from the Blaes85 expression for <math>~W/W_0</math>.  On the other hand, when Blaes refers to the modulus of the amplitude, he includes this leading "unity" constant in evaluating the "real" component of his expression.  I do not yet fully understand why both ways of viewing the eigenfunction's amplitude &#8212; that is, both with and without including the unity term &#8212; can be physically relevant.
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<li>
As a small extension of the Blaes85 analysis, we should determine what the eigenfunction is for the ''density'' perturbation, rather than for the "enthalpy" perturbation, and see how well it matches the ''blue'' amplitude and phase curves published by Hadley et al. 
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