source: palm/trunk/TUTORIAL/SOURCE/ocean_version.tex @ 1547

%$Id: ocean_version.tex 1515 2015-01-02 11:35:51Z witha $
\input{header_tmp.tex}
%\input{../header_lectures.tex}

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\usepackage{subfigure}
\usepackage{units}
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\institute{Institute of Meteorology and Climatology, Leibniz UniversitÀt Hannover}
\selectlanguage{english}
\date{last update: \today}
\event{PALM Seminar}
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\title[PALM Ocean Version]{PALM Ocean Version}
\author{PALM group}


% Notes:
% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
\begin{document}

\begin{frame}
\titlepage
\end{frame}

\section{PALM Ocean Version}
\subsection{PALM Ocean Version}

%Folie 01
\begin{frame}
   \frametitle{PALM - Ocean Version - General Features}
   \begin{itemize}
      \item<2->{Ocean and atmosphere version are sharing the same code.}
      \item<3->{The ocean version is switched on by setting the  +inipar - parameter:\\\quad{\tiny \texttt{ocean = .TRUE.}}}
      \item<4->{There are only few parts in the code which differ between both versions. In the ocean version:}
      \begin{itemize}
         \item<5->{an additional prognostic equation for salinity is solved,}
         \item<6->{in the buoyancy term (w-equation) and the stability-related terms (SGS-TKE-equation), potential temperature is replaced by potential density,}
         \item<7->{density is calculated from the nonlinear equation of state for seawater. So far, only the initial hydrostatic pressure is entered into this equation.}
      \end{itemize}
   \end{itemize}
\end{frame}

%Folie 02
\begin{frame}
   \frametitle{PALM - Ocean Version - Equations}
   \vspace{15pt}

   \tikzstyle{white} = [rectangle, text width=0.9\textwidth, font=\normalsize]
   \tikzstyle{space} = [rectangle, text width=0.01\textwidth, font=\normalsize]
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   \tikzstyle{red} = [rectangle, draw, color=red, text width=0.28\textwidth, minimum size=40pt, font=\normalsize]



   \begin{tikzpicture}[auto, node distance=0]
      \uncover<1->{\node [white] (first) {
      Momentum:
      \begin{align*}
        \frac{\partial \bar{u}_i}{\partial t} =& - \frac{\partial \bar{u}_k \bar{u}_i}{\partial x_k} - \frac{1}{\rho_0} \frac{\partial \bar{p}^*}{\partial x_i} - \varepsilon_{ijk} f_{j} (\bar{u}_k-\bar{u}_{k_g}) - \delta_{i3} g \frac{\bar{\rho}- \tilde{\bar{\rho}}}{\rho_{ref}} - \frac{\partial \overline{u'_k u'_i}}{\partial x_k}\\
      \intertext{Potential Temperature:}
        \frac{\partial \bar{\theta}}{\partial t} =& - \frac{\partial \bar{u}_k \bar{\theta}}{\partial x_k} - \frac{\partial \overline{u'_k \theta'}}{\partial x_k}\\
      \intertext{Salinity:}
        \frac{\partial \bar{S}}{\partial t} =& - \frac{\partial \bar{u}_k \bar{S}}{\partial x_k} - \frac{\partial \overline{u'_k S'}}{\partial x_k}
      \end{align*}
      };}
      \uncover<1->{\node [white, right=-7.3cm of first] (second) {};}

      \uncover<1->{\node [clear, below=-1.2cm of second] (density) {
      Density r = r(S,q,ph) is calculated from the equation of state for seawater using the algorithm from Jackett et al. (2006)
      };}

      \uncover<1->{\node [space, below=1.0cm of density] (space) {};}
      \uncover<1->{\node [space, left=2.35cm of space] (kontis) {\begin{align*}\frac{\partial \bar{u}_k}{\partial x_k} = 0\end{align*}};}
      \uncover<1->{\node [space, right=-0.28cm of space] (reds) {\begin{align*}\frac{\partial^2 \bar{p}^*}{\partial x_{k}^{2}} = \frac{\rho_0}{\Delta t}\frac{\partial \hat{\bar{u}}_k}{\partial x_k}\end{align*}};}

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      \uncover<1->{\node [clear2, left=0.7cm of space2] (konti) {};}
      \uncover<1->{\node [red, right=-0.38cm of space2] (red) {};}

   \end{tikzpicture}

\end{frame}


%Folie 03
\begin{frame}
   \frametitle{PALM - Ocean Version - Grid Structure and Conventions}

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      \uncover<1->{\node [w, right=0.6cm of w73] (w74) {};}

      \path<1-> [line,dotted] (u71.east) -- (u72.west);
      \path<1-> [line,dotted] (u72.east) -- (u73.west);
      \path<1-> [line,dotted] (u73.east) -- (u74.west);
      \path<1-> [line,dotted] (u74.east) -- (u75.west);

      \uncover<1->{\node [scalar, below=0.6cm of scalar61] (scalar71) {};}
      \uncover<1->{\node [scalar, right=0.6cm of scalar71] (scalar72) {};}
      \uncover<1->{\node [scalar, right=0.6cm of scalar72] (scalar73) {};}
      \uncover<1->{\node [scalar, right=0.6cm of scalar73] (scalar74) {};}

      \path<1-> [line,dotted] (w71.south) -- (scalar71.north);
      \path<1-> [line,dotted] (w72.south) -- (scalar72.north);
      \path<1-> [line,dotted] (w73.south) -- (scalar73.north);
      \path<1-> [line,dotted] (w74.south) -- (scalar74.north);



%legende 2D
      \uncover<1->{\node [grid, above=0.6cm of grid11] (2Dlegend00) {};}
      \uncover<1->{\node [grid, right=0.6cm of 2Dlegend00] (2Dlegend10) {};}
      \uncover<1->{\node [grid, above=0.6cm of 2Dlegend00] (2Dlegend01) {};}
      \uncover<1->{\draw [->, color=red] (2Dlegend00.center) -- (2Dlegend10.east);}
      \uncover<1->{\draw [->, color=black] (2Dlegend00.center) -- (2Dlegend01.north);}
      
      \uncover<1->{\node [label, above=0.8cm of 2Dlegend00] (2Dlegend01label) {w,z,k};}
      \uncover<1->{\node [label, right=0.8cm of 2Dlegend00] (2Dlegend10label) {u,x,i};}

      \uncover<1->{\node [scalar, above=0.6cm of grid14] (2Dlegendscalar) {};}
      \uncover<1->{\node [label, right=0.1cm of 2Dlegendscalar] (2Dlegendscalarlabel) {: scalar (e.g. pt)};}
      \uncover<1->{\node [u, above=0.22cm of 2Dlegendscalar] (2Dlegendu) {};}
      \uncover<1->{\node [label, right=0.1cm of 2Dlegendu] (2Dlegendulabel) {: u};}
      \uncover<1->{\node [w, above=0.22cm of 2Dlegendu] (2Dlegendw) {};}
      \uncover<1->{\node [label, right=0.1cm of 2Dlegendw] (2Dlegendwlabel) {: w};}
      
      \uncover<1->{\node [grid, above=0.22cm of 2Dlegendw] (2Dlegendspacing) {};}


%2D Grid Label right
      \uncover<1->{\node [grid, below=0.035cm of grid15] (rightlabelgrid1) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid1] (rightlabelgrid2) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid2] (rightlabelgrid3) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid3] (rightlabelgrid4) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid4] (rightlabelgrid5) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid5] (rightlabelgrid6) {};}
      \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid6] (rightlabelgrid7) {};}

      \uncover<1->{\node[label, right=0.30cm of rightlabelgrid1] (2Dgridlabelnzt1) {\: k = nzt + 1}
         child {node [grid, right=0cm of grid15] {}}
         child {node [grid, right=0cm of u15] {}};}
      
      \uncover<1->{\node[label, right=0.30cm of rightlabelgrid2] (2Dgridlabelnzt2) {\: k = nzt}
         child {node [grid, right=0cm of grid25] {}}
         child {node [grid, right=0cm of u25] {}};}
      
      \uncover<1->{\node[label, right=0.30cm of rightlabelgrid7] (2Dgridlabelnzt7) {\: k = nzb ($\sim0$)}
         child {node [grid, right=0cm of grid75] {}}
         child {node [grid, right=0cm of u75] {}};}
      
      \uncover<1->{\node [grid, right=0.62cm of u25] (rightlabelarrowtop) {};}
      \uncover<1->{\node [grid, right=0.62cm of grid75] (rightlabelarrowbottom) {};}
      \uncover<1->{\draw [->, dotted] (rightlabelarrowtop.south) -- (rightlabelarrowbottom.north);}
      
      \uncover<1->{\node [grid, right=0.2cm of grid25] (grid26) {};}
      \uncover<1->{\node [grid, right=0.6cm of grid26] (grid27) {};}
      \uncover<1->{\node [grid, right=0.3cm of grid27] (grid28) {};}
      \uncover<1->{\draw [->, dashed, color=red] (grid28.center) -- (grid26.center);}
      \uncover<1->{\node [labelred, above=-0.05cm of grid27] (grid27) {(sea sfc)};}

%2D Grid Label left
      \uncover<1->{\node [grid, left=1.4cm of grid11] (leftlabelgrid1) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid1] (leftlabelgrid3) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid3] (leftlabelgrid5) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid5] (leftlabelgrid7) {};}

      \uncover<1->{\node [grid, below=0.22cm of leftlabelgrid1] (leftlabelgrid2) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid2] (leftlabelgrid4) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid4] (leftlabelgrid6) {};}

      \uncover<1->{\node[label, right=0cm of leftlabelgrid2] {$\text{z}=+\frac{\Delta \text{z}}{2}$};}
      \uncover<1->{\node[label, right=0cm of leftlabelgrid3] {$\text{z}=0$};}
      \uncover<1->{\node[label, right=0cm of leftlabelgrid4] {$\text{z}=-\frac{\Delta \text{z}}{2}$};}
      \uncover<1->{\node[label, right=0cm of leftlabelgrid5] {$\text{z}=-\Delta \text{z}$};}
      \uncover<1->{\node[label, right=0cm of leftlabelgrid7] {$\text{z}=-2\Delta \text{z}$};}

      \uncover<1->{\node [grid, left=0.22cm of grid11] (leftarrowgrid1) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid1] (leftarrowgrid3) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid3] (leftarrowgrid5) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid5] (leftarrowgrid7) {};}

      \uncover<1->{\node [grid, below=0.22cm of leftarrowgrid1] (leftarrowgrid2) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid2] (leftarrowgrid4) {};}
      \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid4] (leftarrowgrid6) {};}

      \uncover<1->{\draw [->, dotted] (u11.west) -- (leftarrowgrid2.east);}
      \uncover<1->{\draw [->, dotted] (grid21.west) -- (leftarrowgrid3.east);}
      \uncover<1->{\draw [->, dotted] (u21.west) -- (leftarrowgrid4.east);}
      \uncover<1->{\draw [->, dotted] (grid31.west) -- (leftarrowgrid5.east);}
      \uncover<1->{\draw [->, dotted] (grid41.west) -- (leftarrowgrid7.east);}

      \uncover<1->{\node [grid, below=0.035cm of grid41] (leftlabelarrowtopbase) {};}
      \uncover<1->{\node [grid, left=1.058cm of leftlabelarrowtopbase] (leftlabelarrowtop) {};}
      \uncover<1->{\node [grid, left=1.058cm of grid71] (leftlabelarrowbottom) {};}
      \uncover<1->{\draw [->, dotted] (leftlabelarrowtop.south) -- (leftlabelarrowbottom.north);}

%2D textbox
      \uncover<2->{\node [2dtextbox, below=0.25cm of u43] (2dtextbox) {
         z=0 (sea surface) is assumed at the \textbf{model top}\\ 
         (vertical grid index k=nzt on the w-grid),\\ 
         with negative values of z indicating the depth.
      };}

%------------------------------------3D--------------------------

%grid
      \uncover<1->{\node [grid, right=5.0cm of grid11] (2grid11) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid11] (2grid12) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid12] (2grid13) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid13] (2grid14) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid14] (2grid15) {};}
      
      \uncover<1->{\node [grid, below=0.9cm of 2grid11] (2grid21) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid21] (2grid22) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid22] (2grid23) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid23] (2grid24) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid24] (2grid25) {};}
      
      \uncover<1->{\node [grid, below=0.9cm of 2grid21] (2grid31) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid31] (2grid32) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid32] (2grid33) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid33] (2grid34) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid34] (2grid35) {};}
      
      \uncover<1->{\node [grid, below=0.9cm of 2grid31] (2grid41) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid41] (2grid42) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid42] (2grid43) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid43] (2grid44) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid44] (2grid45) {};}
      
      \uncover<1->{\node [grid, below=0.9cm of 2grid41] (2grid51) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid51] (2grid52) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid52] (2grid53) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid53] (2grid54) {};}
      \uncover<1->{\node [grid, right=0.9cm of 2grid54] (2grid55) {};}


      \fill [fill=blue!20] (2grid12.center)  -- (2grid21.center) -- (2grid51.center) -- (2grid54.center) -- (2grid24.center) -- (2grid15.center);
      \fill [fill=blue!50] (2grid15.center)  -- (2grid24.center) -- (2grid54.center) -- (2grid45.center) -- (2grid15.center);

      \path<1-> [line] (2grid21.center) -- (2grid51.center);
      \path<1-> [line] (2grid51.center) -- (2grid54.center);
      \path<1-> [line] (2grid54.center) -- (2grid24.center);
      \path<1-> [line] (2grid24.center) -- (2grid21.center);
      
      \path<1-> [line,dashed] (2grid42.center) -- (2grid12.center);
      \path<1-> [line,dashed] (2grid42.center) -- (2grid45.center);
      \path<1-> [line] (2grid45.center) -- (2grid15.center);
      \path<1-> [line] (2grid15.center) -- (2grid12.center);
      
      \path<1-> [line] (2grid21.center) -- (2grid12.center);
      \path<1-> [line] (2grid24.center) -- (2grid15.center);
      \path<1-> [line] (2grid54.center) -- (2grid45.center);
      \path<1-> [line,dashed] (2grid42.center) -- (2grid51.center);


%legende 3D
      \uncover<1->{\node [grid, above=0.6cm of 2grid12] (3Dlegend00) {};}
      \uncover<1->{\node [grid, right=0.6cm of 3Dlegend00] (3Dlegend10) {};}
      \uncover<1->{\node [grid, above=0.6cm of 3Dlegend00] (3Dlegend01) {};}
      \uncover<1->{\draw [->, color=red] (3Dlegend00.center) -- (3Dlegend10.east);}
      \uncover<1->{\draw [->, color=black] (3Dlegend00.center) -- (3Dlegend01.north);}
      
      \uncover<1->{\node [grid, right=0.2cm of 3Dlegend00] (3Dlegend010base) {};}
      \uncover<1->{\node [grid, above=0.2cm of 3Dlegend010base] (3Dlegend010) {};}
      \uncover<1->{\draw [->, color=blue] (3Dlegend00.center) -- (3Dlegend010.center);}
      
      \uncover<1->{\node [label, above=0.8cm of 3Dlegend00] (3Dlegend001label) {w,z,k};}
      \uncover<1->{\node [label, right=0.8cm of 3Dlegend00] (3Dlegend100label) {u,x,i};}
      \uncover<1->{\node [label, right=0cm of 3Dlegend010] (3Dlegend010label) {v,y,j};}

%mini koordinaten 3D
      \uncover<1->{\node [grid, right=0.375cm of 2grid11] (3Dkoordgrid11base) {};}
      \uncover<1->{\node [grid, below=0.375cm of 3Dkoordgrid11base] (3Dkoordgrid11) {};}

      \uncover<1->{\node [grid, below=0.375cm of 2grid13] (3Dkoord1base) {};}
      
      \uncover<1->{\node [grid, right=0.375cm of 2grid31] (3Dkoord2base) {};}
      
      \uncover<1->{\node [grid, right=0.375cm of 2grid42] (3Dkoord3basebase) {};}
      \uncover<1->{\node [grid, above=0.375cm of 3Dkoord3basebase] (3Dkoord3base) {};}
     
      \uncover<1->{\node [grid, left=0.375cm of 2grid24] (3Dkoord4basebase) {};}
      \uncover<1->{\node [grid, below=0.375cm of 3Dkoord4basebase] (3Dkoord4base) {};}
      
      \uncover<1->{\node [grid, left=0.375cm of 2grid35] (3Dkoord5base) {};}
      
      \uncover<1->{\node [grid, above=0.375cm of 2grid53] (3Dkoord6base) {};}
      
      \uncover<1->{\node [grid, right=0.9cm of 2grid32] (3Dkoord7base) {};}


      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord1base] (3Dkoord1x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord1base] (3Dkoord1x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord1base] (3Dkoord1z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord1base] (3Dkoord1z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord1base] (3Dkoord1y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord1y1base] (3Dkoord1y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord1base] (3Dkoord1y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord1y2base] (3Dkoord1y2) {};}
      \uncover<1->{\draw [<->, color=red] (3Dkoord1x1.center) -- (3Dkoord1x2.center);}
      \uncover<1->{\draw [<->, color=blue] (3Dkoord1y1.center) -- (3Dkoord1y2.center);}
      \uncover<1->{\draw [<-, color=black] (3Dkoord1z1.center) -- (3Dkoord1base.center);}
      \uncover<1->{\node [label, right=0.2cm of 3Dkoord1y1] (3Dkoord1baselabel) {$\text{w}_{\text{i,j,k}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord2base] (3Dkoord2x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord2base] (3Dkoord2x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord2base] (3Dkoord2z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord2base] (3Dkoord2z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord2base] (3Dkoord2y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord2y1base] (3Dkoord2y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord2base] (3Dkoord2y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord2y2base] (3Dkoord2y2) {};}
      \uncover<1->{\draw [->, color=red] (3Dkoord2base.center) -- (3Dkoord2x2.center);}
      \uncover<1->{\draw [<->, color=blue] (3Dkoord2y1.center) -- (3Dkoord2y2.center);}
      \uncover<1->{\draw [<->, color=black] (3Dkoord2z1.center) -- (3Dkoord2z2.center);}
      \uncover<1->{\node [label, below=0cm of 3Dkoord2z1] (3Dkoord2baselabel) {$\text{u}_{\text{i,j,k}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord3base] (3Dkoord3x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord3base] (3Dkoord3x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord3base] (3Dkoord3z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord3base] (3Dkoord3z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord3base] (3Dkoord3y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord3y1base] (3Dkoord3y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord3base] (3Dkoord3y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord3y2base] (3Dkoord3y2) {};}
      \uncover<1->{\draw [<->, color=red] (3Dkoord3x1.center) -- (3Dkoord3x2.center);}
      \uncover<1->{\draw [->, color=blue] (3Dkoord3base.center) -- (3Dkoord3y2.center);}
      \uncover<1->{\draw [<->, color=black] (3Dkoord3z1.center) -- (3Dkoord3z2.center);}
      \uncover<1->{\node [label, right=0.2cm of 3Dkoord3y1] (3Dkoord3baselabel) {$\text{v}_{\text{i,j,k}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord4base] (3Dkoord4x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord4base] (3Dkoord4x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord4base] (3Dkoord4z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord4base] (3Dkoord4z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord4base] (3Dkoord4y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord4y1base] (3Dkoord4y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord4base] (3Dkoord4y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord4y2base] (3Dkoord4y2) {};}
      \uncover<1->{\draw [<->, color=red] (3Dkoord4x1.center) -- (3Dkoord4x2.center);}
      \uncover<1->{\draw [<-, color=blue] (3Dkoord4y1.center) -- (3Dkoord4base.center);}
      \uncover<1->{\draw [<->, color=black] (3Dkoord4z1.center) -- (3Dkoord4z2.center);}
      \uncover<1->{\node [label, left=0.2cm of 3Dkoord4y2] (3Dkoord4baselabel) {$\text{v}_{\text{i,j+1,k}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord5base] (3Dkoord5x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord5base] (3Dkoord5x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord5base] (3Dkoord5z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord5base] (3Dkoord5z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord5base] (3Dkoord5y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord5y1base] (3Dkoord5y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord5base] (3Dkoord5y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord5y2base] (3Dkoord5y2) {};}
      \uncover<1->{\draw [<-, color=red] (3Dkoord5x1.center) -- (3Dkoord5base.center);}
      \uncover<1->{\draw [<->, color=blue] (3Dkoord5y1.center) -- (3Dkoord5y2.center);}
      \uncover<1->{\draw [<->, color=black] (3Dkoord5z1.center) -- (3Dkoord5z2.center);}
      \uncover<1->{\node [label, below=0cm of 3Dkoord5z1] (3Dkoord5baselabel) {$\text{u}_{\text{i+1,j,k}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord6base] (3Dkoord6x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord6base] (3Dkoord6x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord6base] (3Dkoord6z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord6base] (3Dkoord6z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord6base] (3Dkoord6y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord6y1base] (3Dkoord6y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord6base] (3Dkoord6y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord6y2base] (3Dkoord6y2) {};}
      \uncover<1->{\draw [<->, color=red] (3Dkoord6x1.center) -- (3Dkoord6x2.center);}
      \uncover<1->{\draw [<->, color=blue] (3Dkoord6y1.center) -- (3Dkoord6y2.center);}
      \uncover<1->{\draw [->, color=black] (3Dkoord6base.center) -- (3Dkoord6z2.center);}
      \uncover<1->{\node [label, right=0.2cm of 3Dkoord6y1] (3Dkoord6baselabel) {$\text{w}_{\text{i,j,k-1}}$};}

      \uncover<1->{\node [grid, left=0.15cm of 3Dkoord7base] (3Dkoord7x1) {};}
      \uncover<1->{\node [grid, right=0.15cm of 3Dkoord7base] (3Dkoord7x2) {};}
      \uncover<1->{\node [grid, below=0.15cm of 3Dkoord7base] (3Dkoord7z1) {};}
      \uncover<1->{\node [grid, above=0.15cm of 3Dkoord7base] (3Dkoord7z2) {};}
      \uncover<1->{\node [grid, left=0.03cm of 3Dkoord7base] (3Dkoord7y1base) {};}
      \uncover<1->{\node [grid, below=0.03cm of 3Dkoord7y1base] (3Dkoord7y1) {};}
      \uncover<1->{\node [grid, right=0.03cm of 3Dkoord7base] (3Dkoord7y2base) {};}
      \uncover<1->{\node [grid, above=0.03cm of 3Dkoord7y2base] (3Dkoord7y2) {};}
      \uncover<1->{\draw [<->, color=red] (3Dkoord7x1.center) -- (3Dkoord7x2.center);}
      \uncover<1->{\draw [<->, color=blue] (3Dkoord7y1.center) -- (3Dkoord7y2.center);}
      \uncover<1->{\draw [<->, color=black] (3Dkoord7z1.center) -- (3Dkoord7z2.center);}
      \uncover<1->{\node [label, right=0.2cm of 3Dkoord7y1] (3Dkoord7baselabel) {$\text{s}_{\text{i,j,k}}$};}
   \end{tikzpicture}
\end{frame}


%Folie 04
\begin{frame}
   \frametitle{PALM - Ocean Version - Boundary Conditions}
   
   The following boundary conditions should be used for the ocean version. Some of them are not set by default, so please set them manually.\\
   
   \begin{itemize}
      \item<2->{Ocean surface (z=0):}
      \begin{itemize}
         \item<2->{Fluxes should be given at the ocean surface for all quantities. This requires parameter\\\quad{\tiny \texttt{top\_momentum\_flux\_u = ..., top\_momentum\_flux\_v = ..., bc\_uv\_t = ‘neumann’}}}
         \item<3->{Momentum:\\\quad{\tiny \texttt{use\_top\_fluxes = .TRUE.}}}
         \item<4->{Temperature:\\\quad{\tiny \texttt{top\_heatflux = ..., bc\_pt\_t = ‘neumann’}}}
         \item<5->{Salinity:\\\quad{\tiny \texttt{top\_salinityflux = ..., bc\_sa\_t = ‘neumann’}}}
      \end{itemize}
      \item<6->{Ocean bottom (z=-...)}
      \begin{itemize}
         \item<6->{A Prandtl-layer should be used at the bottom:\\\quad{\tiny \texttt{prandtl\_layer = .TRUE.}}}
      \end{itemize}
   \end{itemize}
\end{frame}


%Folie 05
\begin{frame}
   \frametitle{PALM - Ocean Version - Further Settings}
   \begin{itemize}
      \item<2->{Initial profiles:}
      \begin{itemize}
         \item<2->{The ocean version can only use:\\\quad{\tiny \texttt{initializing\_actions = ‘set\_constant\_profiles’}}}
         \item<3->{Profiles are constructed piecewise linear \underline{from the top} (surface), using parameters (e.g.):\\\quad{\tiny \texttt{pt\_surface = ..., pt\_initial\_gradient = ..., pt\_initial\_gradient\_level = ...}}}
      \end{itemize}
      \item<4->{Random perturbations:}
      \begin{itemize}
         \item<4->{Random perturbations are by default applied to the upper third of the model domain!}
      \end{itemize}
   \end{itemize}
\end{frame}

%Folie 06
\begin{frame}
   \frametitle{PALM - Ocean Version - Final Remarks}
   \begin{itemize}
      \item<2->{The ocean version of PALM has not been tested sufficiently so far! Only some plausibility checks have been done.}
      \item<3->{Please carefully check the results and please also check the code.}
      \item<4->{Effects of surface waves (Langmuir circulation, wave breaking) are not included in the standard code.}
   \end{itemize}
\end{frame}

\end{document}