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\institute{Institut für Meteorologie und Klimatologie, Leibniz Universität Hannover}
\date{last update: \today}
\event{PALM Seminar}
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\title[Exercise 1: Convection Between Plates]{Exercise 1: Convection Between Plates}
\author{Siegfried Raasch}

\begin{document}

% Folie 1
\begin{frame}
\titlepage
\end{frame}

\section{Exercise}
\subsection{Exercise}

% Folie 2
\begin{frame}
   \frametitle{Exercise 1: Convection Between Plates}
   
   Please try to carry out a run with following initial and boundary conditions and create the required output.
   \begin{itemize}
      \scriptsize
	   \item<2-> The simulation should represent a stationary convective boundary layer between two uniformly heated/cooled plates with zero mean flow.
	   \item<3-> A free-slip condition for velocity shall be used at the bottom and top boundary.
	   \item<4-> The sensible heat flux at the bottom and top boundary shall be constant throughout the simulation.
   \end{itemize}   
   \onslide<5-> Simulation features:
   \begin{itemize}
      \scriptsize
	   \item<6-> domain size: about $\unit[2000 \times 2000 \times 1000]{m^3}$ ($x$/$y$/$z$)
	   \item<7-> grid size: $\unit[50]{m}$ equidistant
	   \item<8-> simulated time:	$\unit[3600]{s}$
	   \item<9-> surface heatflux: $\unit[0.1]{K\ m\ s^{-1}}$
	   \item<10-> heatflux at top: $\unit[0.1]{K\ m\ s^{-1}}$
	   \item<11-> initial temperature: $\unit[300]{K}$ everywhere
	   \item<12-> initial velocity: zero everywhere
   \end{itemize}  
\end{frame}

% Folie 3
\begin{frame}
   \frametitle{Questions to be Answered:}
   
   \begin{itemize}
   \item<1-> How does the flow field look like after 60 minutes of simulated time? (What kind of output do you need to answer this?)
   \item<2-> How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like?
   \item<3-> Is it really a large-eddy simulation, i.e. are the subgrid-scale fluxes much smaller than the resolved-scale fluxes? (How long should the averaging time interval be?)
   \item<4-> How do the total kinetic energy and the maximum velocity components change in time? Has the flow become stationary?
   \item<5-> Has the domain size and grid size been chosen appropriately?
   \end{itemize}

\end{frame}
	
% Folie 4
\begin{frame}
   \frametitle{Hints (I)}
   \scriptsize
   
   PALM parameter names are displayed by courier style, e.g. \textcolor{blue}{\texttt{end\_time}}.\\

   \begin{itemize}
      \item<2-> Domain size
      \begin{itemize}
         \scriptsize
         \item[-]<2-> Is controlled by grid size (\textcolor{blue}{\texttt{dx}}, \textcolor{blue}{\texttt{dy}}, \textcolor{blue}{\texttt{dz}}) and number of grid points (\textcolor{blue}{\texttt{nx}}, \textcolor{blue}{\texttt{ny}}, \textcolor{blue}{\texttt{nz}}). Since the first grid point along each of the directions has index 0, the total number of grid points used are \textcolor{blue}{\texttt{nx}}+1, \textcolor{blue}{\texttt{ny}}+1, \textcolor{blue}{\texttt{nz}}+1. The total domain size in case of cyclic horizontal boundary conditions is (\textcolor{blue}{\texttt{nx}}+1)*\textcolor{blue}{\texttt{dx}}, (\textcolor{blue}{\texttt{ny}}+1)*\textcolor{blue}{\texttt{dy}}.
      \end{itemize}
      
      \item<3-> Initial profiles
      \begin{itemize}
         \scriptsize
         \item[-]<3-> Constant with height. See parameter \textcolor{blue}{\texttt{initializing\_actions}} for available initialization methods. See \textcolor{blue}{\texttt{ug\_surface}}, \textcolor{blue}{\texttt{vg\_surface}} and \textcolor{blue}{\texttt{pt\_surface}} for initial values of velocity and potential temperature.
      \end{itemize}
      
      \item<4-> Boundary conditions
       \begin{itemize}
         \scriptsize
         \item[-]<4-> For velocity, see \textcolor{blue}{\texttt{bc\_uv\_b}} and \textcolor{blue}{\texttt{bc\_uv\_t}}. See also \textcolor{blue}{\texttt{prandtl\_layer}}, because Neumann conditions don’t allow to use a Prandtl-layer.
         \item[-]<5-> For temperature / heat flux, see \textcolor{blue}{\texttt{surface\_heatflux}} and \textcolor{blue}{\texttt{top\_heatflux}}. Prescribing of heat flux at the boundary requires a Neumann boundary condition for temperature, see \textcolor{blue}{\texttt{bc\_pt\_b}} and \textcolor{blue}{\texttt{bc\_pt\_t}}.
         \item[-]<6-> Use a Neumann condition also for the perturbation pressure both at the bottom and the top (\textcolor{blue}{\texttt{bc\_p\_b}}, \textcolor{blue}{\texttt{bc\_p\_t}}).
      \end{itemize}     
      
      \item<7-> Simulation time
      \begin{itemize}
         \scriptsize
         \item[-]<7-> See parameter \textcolor{blue}{\texttt{end\_time}}.
      \end{itemize}
      
   \end{itemize}

\end{frame}

% Folie 5
\begin{frame}
   \frametitle{Hints (II)}
   \footnotesize
   
   Hints for data output.
   
   \begin{itemize}
   
      \item<2-> Variables
      \begin{itemize}
         \footnotesize
         \item[-]<2-> Output variables are chosen with parameters \textcolor{blue}{\texttt{data\_output}} (3d-data or 2d-cross-sections) and \textcolor{blue}{\texttt{data\_output\_pr}} (profiles).
      \end{itemize}

      \item<3-> Output intervals
      \begin{itemize}
         \footnotesize
         \item[-]<3-> Output intervals are set with parameter \textcolor{blue}{\texttt{dt\_data\_output}}. This parameter affects all output (cross-sections, profiles, etc.). Individual temporal intervals for the different output quantities can be assigned using parameters \textcolor{blue}{\texttt{dt\_do3d}}, \textcolor{blue}{\texttt{dt\_do2d\_xy}}, \textcolor{blue}{\texttt{dt\_do2d\_xz}}, \textcolor{blue}{\texttt{dt\_do2d\_yz}}, \textcolor{blue}{\texttt{dt\_dopr}}, etc. 
      \end{itemize}
      
      \item<4-> Time averaging
      \begin{itemize}
         \footnotesize
         \item[-]<4-> Time averaging is controlled with parameters  \textcolor{blue}{\texttt{averaging\_interval}},  \textcolor{blue}{\texttt{averaging\_interval\_pr}},  \textcolor{blue}{\texttt{dt\_averaging\_input}},  \textcolor{blue}{\texttt{dt\_averaging\_input\_pr}}.
      \end{itemize}

   \end{itemize}

\end{frame}

% Folie 6
\begin{frame}
   \frametitle{Further Hints}

   \onslide<2-> You will find some more detailed information to solve this exercise in the PALM-online-documentation under:\\
   \ \\
   \small\url{http://palm.muk.uni-hannover.de/wiki/doc/app/examples/cbl}\\
   \ \\
   \normalsize (Attention: This documentation is for atmospheric convection with free upper lid.)
   \ \\
   \ \\
   \normalsize Please also see under\\
   \ \\
   \small\url{http://palm.muk.uni-hannover.de/wiki/doc/app/netcdf}\\
   \ \\
   \normalsize where the complete PALM netCDF-data-output and the respective steering parameters are described.

\end{frame}

% Folie 7
\begin{frame}
   \frametitle{How to Start?}

   \begin{itemize}
      \item<2-> Create a data directory for a new run:\\
	   \quad \texttt{cd \~{}/palm/current\_version}\\
	   \quad \texttt{mkdir -p JOBS/uniform\_plates/INPUT}
	   
	   \item<3-> Create the parameter file and set the required parameters in\\
 	   \quad \texttt{JOBS/uniform\_plates/INPUT/uniform\_plates\_p3d}
 	   
 	   \item<4-> Start the run with \texttt{mrun-command}\\
	   \quad \texttt{mrun -d uniform\_plates -h <hi> -K parallel ...}\\
	   and analyze the output files.

   \end{itemize}
   
   \ \\
   
   \onslide<5-> \huge \centering \textcolor{blue}{Good Luck!}

\end{frame}

% Folie 8
\section{Results}
\subsection{Results}

\begin{frame}
   \frametitle{$xy$-cross sections (instantaneous)}
   \begin{center}
      \includegraphics[width=0.42\textwidth]{exercise_cbl_figures/xy_w_100.eps}
      \includegraphics[width=0.42\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\
      \includegraphics[width=0.42\textwidth]{exercise_cbl_figures/xy_w_750.eps}
   \end{center}
\end{frame}

% Folie 9
\begin{frame}
   \frametitle{$xz$-cross sections ($\unit[900]{s}$ average)}
   \begin{center}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y250m.eps}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y500m.eps}\\
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y750m.eps}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y1000m.eps}
   \end{center}
\end{frame}

% Folie 10
\begin{frame}
   \frametitle{Vertical profiles (I)}
   \begin{center}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_pt.eps}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_wpt.eps}
   \end{center}
\end{frame}

% Folie 11
\begin{frame}
   \frametitle{LES?}
   \begin{center}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_wpt2.eps}
      \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_wpt_resolved.eps}
   \end{center}
\end{frame}

% Folie 12
\begin{frame}
   \frametitle{Time series (I)}
   \begin{center}
      \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/ts.eps}
   \end{center}
\end{frame}

% Folie 13
\begin{frame}
   \frametitle{Time series (II)}
   \begin{center}
      \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/ts2.eps}
   \end{center}
\end{frame}
\end{document}