[cig-commits] r8150 - doc/CitcomS/manual

tan2 at geodynamics.org tan2 at geodynamics.org
Thu Oct 18 16:11:09 PDT 2007


Author: tan2
Date: 2007-10-18 16:11:08 -0700 (Thu, 18 Oct 2007)
New Revision: 8150

Modified:
   doc/CitcomS/manual/citcoms.lyx
Log:
Add eqns to non-dimensionalize phase change depth and clapeyron slope

Modified: doc/CitcomS/manual/citcoms.lyx
===================================================================
--- doc/CitcomS/manual/citcoms.lyx	2007-10-18 21:32:02 UTC (rev 8149)
+++ doc/CitcomS/manual/citcoms.lyx	2007-10-18 23:11:08 UTC (rev 8150)
@@ -843,7 +843,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-\rho c_{P}\left(T_{,t}+u_{i}T_{,i}\right)=\rho c_{P}\kappa T_{,ii}+\rho\alpha gu_{r}\left(T+T_{0}\right)+\Phi+\rho Q_{L}+\rho H\label{eq:conservation of energy}\end{equation}
+\rho c_{P}\left(T_{,t}+u_{i}T_{,i}\right)=\rho c_{P}\kappa T_{,ii}+\rho\alpha gu_{r}\left(T+T_{0}\right)+\Phi+\rho\left(Q_{L,t}+u_{i}Q_{L,i}\right)+\rho H\label{eq:conservation of energy}\end{equation}
 
 \end_inset
 
@@ -1207,6 +1207,26 @@
 \end_layout
 
 \begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
+d_{ph}=R_{0}d_{ph}^{'}\label{eq:dph dim}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align right
+\begin_inset Formula \begin{equation}
+\gamma_{ph}=\frac{\rho_{0}g_{0}R_{0}}{\Delta T}\gamma_{ph}^{'}\label{eq:gammaph dim}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
 \noindent
 where 
 \begin_inset Formula $\rho_{0}$
@@ -1265,7 +1285,7 @@
 \begin_layout Standard
 \align right
 \begin_inset Formula \begin{equation}
-\bar{\rho}c_{P}\left(T_{,t}+u_{i}T_{,i}\right)\left(1+2\Gamma\left(1-\Gamma\right)\frac{\gamma_{ph}^{2}}{d_{ph}}\frac{Rab}{Ra}Di\left(T+T_{0}\right)\right)=\bar{\rho}c_{P}\kappa T_{,ii}+\rho\alpha gu_{r}Di\left(T+T_{0}\right)\left(1+2\Gamma\left(1-\Gamma\right)\frac{\gamma_{ph}}{d_{ph}}\frac{Rab}{Ra}\right)+\frac{Ra}{Di}\Phi+\bar{\rho}H\label{eq:non-dimensional energy eqn}\end{equation}
+\bar{\rho}c_{P}\left(T_{,t}+u_{i}T_{,i}\right)\left(1+2\Gamma\left(1-\Gamma\right)\frac{\gamma_{ph}^{2}}{d_{ph}}\frac{Rab}{Ra}Di\left(T+T_{0}\right)\right)=\bar{\rho}c_{P}\kappa T_{,ii}+\rho\alpha gu_{r}Di\left(T+T_{0}\right)\left(1+2\Gamma\left(1-\Gamma\right)\frac{\gamma_{ph}}{d_{ph}}\frac{Rab}{Ra}\right)+\frac{Di}{Ra}\Phi+\bar{\rho}H\label{eq:non-dimensional energy eqn}\end{equation}
 
 \end_inset
 



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