Editing Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase (section)

=Simple Rotation Profiles=
In support of the broad scope of problems that are discussed within this [[H_BookTiledMenu#Tiled_Menu|online Hypertext_Book]], a [[AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|separate chapter]] provides a brief review of the variety of ''[[AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|Simple Rotation Profiles]]'' that are typically referenced and/or employed across the research community in discussions of astrophysical fluid flows.  The [[#See_Also|Hadley &amp; Imamura collaboration]] has explored the stability of initially axisymmetric, toroidal configurations that have a variety of angular velocity profiles.  As has been [[#Specifics_of_Database|pointed out, above]], each of their angular velocity profiles, <math>~\Omega(\varpi)</math>, is uniquely prescribed via the choice of the power-law index, <math>~q</math>, through the expression (see, for example, equation 6 of [http://adsabs.harvard.edu/abs/2014Ap%26SS.353..191H Paper II]),
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<math>~\frac{\Omega(\varpi)}{\Omega_0}</math>
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<math>~=</math>
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<math>~\biggl(\frac{\varpi}{\varpi_0}\biggr)^{-q} \, ,</math>
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where the subscript, "0", denotes the location of the density and pressure maximum inside the initial, equilibrium toroidal configuration. All of these fall within the category of ''Simple Rotation Profiles,'' in the sense we have reviewed.  However, care must be taken when drawing parallels between our review and the discussions presented by the [[#See_Also|Hadley & Imamura collaboration]] because our review also refers to a power-law index, <math>~q</math> &#8212; for clarity, here,  let's call it, <math>~q_\mathrm{H\_Book}</math> &#8212; but its definition is different from the one used by the Hadley &amp; Imamura collaboration &#8212; for clarity, call it, <math>~q_\mathrm{HI}</math>.  In order to relate one set of discussions to the other requires the mapping,
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<math>~q_\mathrm{HI}~~~\leftrightarrow~~~(2-q_\mathrm{H\_Book}) \, .</math>
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