[cig-commits] r6714 - geodyn/3D/MoSST/trunk/doc

[sue at geodynamics.org]

Author: sue
Date: 2007-04-27 12:47:42 -0700 (Fri, 27 Apr 2007)
New Revision: 6714

Modified:
   geodyn/3D/MoSST/trunk/doc/mosst.lyx
Log:
added more equations

Modified: geodyn/3D/MoSST/trunk/doc/mosst.lyx
===================================================================
--- geodyn/3D/MoSST/trunk/doc/mosst.lyx	2007-04-27 19:31:10 UTC (rev 6713)
+++ geodyn/3D/MoSST/trunk/doc/mosst.lyx	2007-04-27 19:47:42 UTC (rev 6714)
@@ -335,10 +335,6 @@
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula $ $
-\end_inset
-
-
 \begin_inset Formula $\rho:$
 \end_inset
 
@@ -405,7 +401,7 @@
 \end_layout
 
 \begin_layout Paragraph*
-Parameters:
+Parameters
 \end_layout
 
 \begin_layout Standard
@@ -413,7 +409,7 @@
 \begin_inset Formula $R_{a}=\frac{\alpha g_{o}\Delta TD}{\nu\Omega}$
 \end_inset
 
- 
+
 \end_layout
 
 \begin_layout Standard
@@ -440,34 +436,49 @@
  
 \end_layout
 
+\begin_layout Subsubsection*
+Dimensionless equations
+\end_layout
+
 \begin_layout Standard
-Dimensionless equations:
+\begin_inset Formula \[
+E_{c}\left(\frac{\partial\mathrm{\mathbf{u}}}{\partial t}+\mathrm{\mathbf{u}}\cdot\nabla\mathrm{\mathbf{u}}-\nabla^{2}\mathrm{\mathbf{u}}\right)+2\hat{\mathrm{\mathbf{z}\times\mathbf{u}=-\nabla\mathit{P+R_{a}\frac{\mathrm{\mathbf{r}}}{r_{o}}\mathit{\Upsilon+\frac{1}{P_{m}}\left(\nabla\times\mathrm{\mathbf{B}}\right)\times\mathrm{\mathbf{B}}}}}}\]
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 \begin_inset Formula \[
-E_{c}\left(\frac{\partial\mathrm{\mathbf{u}}}{\partial t}+\mathrm{\mathbf{u}}\bullet\bigtriangledown\mathrm{\mathbf{u}}-\bigtriangledown^{2}\mathrm{\mathbf{u}}\right)+2\hat{\mathrm{\mathbf{z}\times u=-\bigtriangledown\mathit{P+R_{a}\frac{\mathrm{\mathbf{r}}}{r_{o}}\mathit{\Upsilon+\frac{1}{P_{m}}\left(\bigtriangledown\times\mathrm{\mathbf{B}}\right)\times\mathrm{\mathbf{B}}}}}}\]
+\frac{\partial\mathrm{\mathbf{B}}}{\partial t}=\nabla\times\left(\mathbf{u}\times\mathbf{B}\right)+\frac{1}{P_{m}}\nabla^{2}\mathbf{B}\]
 
 \end_inset
 
 
+\begin_inset Formula \[
+\frac{\partial\mathrm{\mathbf{\mathit{T}}}}{\partial t}+\mathbf{u}\cdot\nabla T=\frac{1}{P_{r}}\nabla^{2}T\]
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 \begin_inset Formula \[
-\frac{\partial\mathrm{\mathbf{B}}}{\partial t}\]
+\nabla\cdot\mathbf{u}=0,\,\,\nabla\cdot\mathrm{\mathbf{B}}=0.\]
 
 \end_inset
 
-.
+
 \end_layout
 
 \begin_layout Standard
 The head bar denotes the unit vector.
 \end_layout
 
-\begin_layout Standard
-Kuang?s non-dimensionalization
+\begin_layout Paragraph*
+Kuang's non-dimensionalization
 \end_layout
 
 \begin_layout Standard
@@ -475,55 +486,95 @@
 \end_layout
 
 \begin_layout Standard
-radial of the outer core
+\begin_inset Formula $r_{o}:$
+\end_inset
+
+ radial of the outer core
 \end_layout
 
 \begin_layout Standard
-kinematic viscosity
+\begin_inset Formula $v$
+\end_inset
+
+: kinematic viscosity
 \end_layout
 
 \begin_layout Standard
-magnetic diffusivity
+\begin_inset Formula $\eta:$
+\end_inset
+
+ magnetic diffusivity
 \end_layout
 
 \begin_layout Standard
-thermal diffusivity
+\begin_inset Formula $\kappa:$
+\end_inset
+
+ thermal diffusivity
 \end_layout
 
 \begin_layout Standard
-magnetic permeability
+\begin_inset Formula $\mu:$
+\end_inset
+
+ magnetic permeability
 \end_layout
 
 \begin_layout Standard
-basic rotating rate
+\begin_inset Formula $\Omega:$
+\end_inset
+
+ basic rotating rate
 \end_layout
 
 \begin_layout Standard
-density
+\begin_inset Formula $\rho:$
+\end_inset
+
+ density
 \end_layout
 
 \begin_layout Standard
-thermal expansion coefficient
+\begin_inset Formula $\alpha:$
+\end_inset
+
+ thermal expansion coefficient
 \end_layout
 
-\begin_layout Standard
-Scales:
+\begin_layout Paragraph*
+Scales
 \end_layout
 
 \begin_layout Standard
 length: 
+\begin_inset Formula $r_{o}$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 time: 
+\begin_inset Formula $r_{o}^{2}/\eta$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 velocity: 
+\begin_inset Formula $\eta/r_{o}$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 temperature: 
+\begin_inset Formula $h_{T}r_{o}=r_{o}\frac{-\partial T}{\partial r}\mid_{r=r_{i}}$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard