Editing ThreeDimensionalConfigurations/DescriptionOfRiemannTypeI (section)

==EFE Rotating Cartesian Frame==
Concentric triaxial ellipsoids are defined by the expression,
<table border="0" align="center" cellpadding="5">
<tr>
  <td align="right"><math>P</math></td>
  <td align="center"><math>=</math></td>
  <td align="right"><math>\biggl(\frac{x}{a}\biggr)^2 + \biggl(\frac{y}{b}\biggr)^2 + \biggl(\frac{z}{c}\biggr)^2 \, ,</math></td>
</tr>
</table>
where <math>0 \le P \le 1</math> is a constant.  As viewed from the rotating reference frame, the velocity flow-field everywhere inside <math>(0 \le P < 1)</math>, and on the surface <math>(P = 1)</math> of the Type I Riemann ellipsoid is given by the expression &#8212; see, for example, an [[ThreeDimensionalConfigurations/ChallengesPt6#Riemann_Flow|accompanying discussion of the Riemann flow-field]],

<table border="0" align="center" cellpadding="5">
<tr>
  <td align="right"><math>\mathbf{u}_\mathrm{EFE}</math></td>
  <td align="center"><math>=</math></td>
  <td align="right"><math>
\boldsymbol{\hat\imath} \biggl\{ - \biggl[ \frac{a^2}{a^2 + b^2} \biggr] \zeta_3 y + \biggl[ \frac{a^2}{a^2 + c^2} \biggr] \zeta_2 z \biggr\}
+
\boldsymbol{\hat\jmath} \biggl\{ +\biggl[ \frac{b^2}{a^2 + b^2} \biggr] \zeta_3 x \biggr\}
+
\mathbf{\hat{k}} \biggl\{ - \biggl[ \frac{c^2}{a^2 + c^2} \biggr] \zeta_2 x  \biggr\}
\, .</math>
  </td>
</tr>
</table>
In an [[ThreeDimensionalConfigurations/ChallengesPt6#EFE_Rotating_Frame|accompanying discussion]], we have shown that,
<table border="0" align="center" cellpadding="5">
<tr>
  <td align="right"><math>\mathbf{u}_\mathrm{EFE} \cdot \nabla P</math></td>
  <td align="center"><math>=</math></td>
  <td align="right"><math>0 \, ,</math></td>
</tr>
</table>
which means that, at every location inside and on the surface of the configuration, the velocity vector is orthogonal to a vector that is normal to the ellipsoidal surface at that location.