--- manual/s_overview/appendix_atmos.tex 2001/09/11 14:34:38 1.2 +++ manual/s_overview/appendix_atmos.tex 2001/09/26 14:53:10 1.3 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_atmos.tex,v 1.2 2001/09/11 14:34:38 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_atmos.tex,v 1.3 2001/09/26 14:53:10 cnh Exp $ % $Name: $ \section{Appendix ATMOSPHERE} @@ -78,11 +78,11 @@ \subsubsection{Boundary conditions} The upper and lower boundary conditions are : -\begin{eqnarray*} +\begin{eqnarray} \mbox{at the top:}\;\;p=0 &&\text{, }\omega =\frac{Dp}{Dt}=0 \\ \mbox{at the surface:}\;\;p=p_{s} &&\text{, }\phi =\phi _{topo}=g~Z_{topo} \label{eq:boundary-condition-atmosphere} -\end{eqnarray*} +\end{eqnarray} In $p$-coordinates, the upper boundary acts like a solid boundary ($\omega =0 $); in $z$-coordinates and the lower boundary is analogous to a free surface ($\phi $ is imposed and $\omega \neq 0$). @@ -95,11 +95,11 @@ is not dynamically relevant and can therefore be subtracted from the equations. The equations written in terms of perturbations are obtained by substituting the following definitions into the previous model equations: -\begin{eqnarray*} +\begin{eqnarray} \theta &=&\theta _{o}+\theta ^{\prime } \label{eq:atmos-ref-prof-theta} \\ \alpha &=&\alpha _{o}+\alpha ^{\prime } \label{eq:atmos-ref-prof-alpha}\\ \phi &=&\phi _{o}+\phi ^{\prime } \label{eq:atmos-ref-prof-phi} -\end{eqnarray*} +\end{eqnarray} The reference state (indicated by subscript ``0'') corresponds to horizontally homogeneous atmosphere at rest ($\theta _{o},\alpha _{o},\phi _{o}$) with surface pressure $p_{o}(x,y)$ that satisfies $\phi