[cig-commits] r6341 - mc/3D/CitcomS/trunk/doc/manual

[tan2 at geodynamics.org]

Author: tan2
Date: 2007-03-21 15:46:08 -0700 (Wed, 21 Mar 2007)
New Revision: 6341

Modified:
   mc/3D/CitcomS/trunk/doc/manual/citcoms.lyx
Log:
Added chemical Rayleigh number to the equations

Modified: mc/3D/CitcomS/trunk/doc/manual/citcoms.lyx
===================================================================
--- mc/3D/CitcomS/trunk/doc/manual/citcoms.lyx	2007-03-21 22:45:51 UTC (rev 6340)
+++ mc/3D/CitcomS/trunk/doc/manual/citcoms.lyx	2007-03-21 22:46:08 UTC (rev 6341)
@@ -744,10 +744,6 @@
 
 \begin_layout Standard
 \align right
-\begin_inset Formula $ $
-\end_inset
-
-
 \begin_inset Formula \begin{equation}
 -P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+\delta\rho g\delta_{ir}=0\label{eq:conservation of momentum}\end{equation}
 
@@ -830,7 +826,8 @@
 \end_inset
 
  is time.
- Without phase transitions, the density anomalies are:
+ Without phase transitions and composition variation, the density anomalies
+ are:
 \end_layout
 
 \begin_layout Standard
@@ -920,6 +917,10 @@
 \begin_layout Standard
 \noindent
 where 
+\begin_inset Formula $\rho_{0}$
+\end_inset
+
+is the reference density, 
 \begin_inset Formula $R_{0}$
 \end_inset
 
@@ -976,7 +977,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-Ra=\frac{\rho g\alpha\Delta TR_{0}^{3}}{\eta_{0}\kappa}\label{eq:Ra, a Rayleigh number}\end{equation}
+Ra=\frac{\rho_{0}g\alpha\Delta TR_{0}^{3}}{\eta_{0}\kappa}\label{eq:Ra, a Rayleigh number}\end{equation}
 
 \end_inset
 
@@ -1013,7 +1014,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
--P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+(RaT+R_{b}\Gamma)\delta_{ir}=0\label{eq:16}\end{equation}
+-P_{,i}+(\eta u_{i,j}+\eta u_{j,i})_{,j}+(RaT+Rab\Gamma-RacC)\delta_{ir}=0\label{eq:16}\end{equation}
 
 \end_inset
 
@@ -1033,6 +1034,10 @@
 \begin_layout Standard
 \noindent
 where 
+\emph on
+C
+\emph default
+ is the composition, 
 \begin_inset Formula $d_{ph}$
 \end_inset
 
@@ -1050,16 +1055,20 @@
 
  is the width of a phase transition.
  The phase-change Rayleigh number, 
-\begin_inset Formula $R_{b}$
+\begin_inset Formula $Rab$
 \end_inset
 
-, is defined as:
+, and the chemical Rayleigh number, 
+\begin_inset Formula $Rac$
+\end_inset
+
+, are defined as:
 \end_layout
 
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-R_{b}=\frac{\Delta\rho_{ph}gR_{0}^{3}}{\eta_{0}\kappa}\label{eq:Rb, the phase-change Rayleigh number}\end{equation}
+Rab=Ra\frac{\delta\rho_{ph}}{\rho_{0}}\label{eq:Rab, the phase-change Rayleigh number}\end{equation}
 
 \end_inset
 
@@ -1067,12 +1076,26 @@
 \end_layout
 
 \begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
+Rac=Ra\frac{\delta\rho_{ch}}{\rho_{0}}\label{eq:Rac, a chemical Rayleigh number}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 \noindent
 where 
-\begin_inset Formula $\Delta\rho_{ph}$
+\begin_inset Formula $\delta\rho_{ph}$
 \end_inset
 
- is the density jump across a phase change.
+ is the density jump across a phase change, and 
+\begin_inset Formula $\delta\rho_{ch}$
+\end_inset
+
+ is the density difference between the compositions.
 \end_layout
 
 \begin_layout Section