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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 2: Neutrally Stratified  Boundary Layer]{Exercise 2: Neutrally Stratified  Boundary Layer}
\author{Siegfried Raasch}

\setbeamersize{text margin left=.2cm,text margin right=.2cm}

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

\section{Exercise}
\subsection{Exercise}

% Folie 2
\begin{frame}
   \frametitle{Exercise 2: Neutrally Stratified  Atmospheric Boundary Layer}
   \begin{itemize}
      \item A neutrally stratified atmospheric boundary layer shall be simulated.
      \item<2-> The flow shall be driven by a constant large-scale pressure gradient, i.e. a geostrophic wind.
      \item<3-> At the end of the simulation, turbulence as well as the mean flow should be in a stationary state.
   \end{itemize}
   \onslide<4->\textbf{Simulation features:}
    \begin{itemize}
          \item<4-> geostrophic wind:  \tabto{3cm} $u_\mathrm{g} = \unit[5]{m\ s^{-1}}, v_\mathrm{g} = \unit[0]{m\ s^{-1}}$
          \item<5-> initial velocity:  \tabto{3cm} try constant velocity ($u = u_\mathrm{g}, v = v_\mathrm{g}$, everywhere)\\ 
                    \tabto{3cm} or a mean vertical profile created by the 1D-model
          \item<6-> roughness length:  \tabto{3cm} $z_0 = \unit[0.1]{m}$
    \end{itemize}
\onslide<7->Please choose domain size, grid size and time to be simulated appropriately.
\end{frame}

% Folie 3
\begin{frame}
   \frametitle{Questions to be Answered:}
    \begin{itemize}
       \item<1-> How long do you have to simulate until turbulence / mean flow become stationary?
       \vspace{1em}
       \item<2-> How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like?
       \vspace{1em}
       \item<3-> Is it really a large-eddy simulation, i.e. are the subgrid-scale fluxes much smaller than the resolved-scale fluxes?
       \vspace{1em}
       \item<4-> How do the turbulence spectra of $u$, $v$, $w$ along $x$ and along $y$ look like?\\
                 Can you identify the inertial subrange?
    \end{itemize}
\end{frame}

% Folie 4
 \begin{frame}
    \frametitle{Hints (I)}
     \begin{itemize}
        \item<1-> Please remember hints given for the previous exercise!
        \item<2-> \textbf{Initial profiles:}
        \begin{itemize}
           \tiny
           \item<3-> The 1D-model (\texttt{\textcolor{blue}{initializing\_actions} = 'set\_1d-model\_profiles'}) is mainly controlled by parameters \texttt{\textcolor{blue}{end\_time\_1d}} and \texttt{\textcolor{blue}{damp\_level\_1d}}. Please keep in mind that the profiles from the 1D-model should also be in a stationary state.
           \vspace{0.5em}
            \item<3-> Output of vertical profile data generated by the 1D-model is controlled by parameter \texttt{\textcolor{blue}{dt\_pr\_1d}}. It is in ASCII-format and it is written into a separate file. You can include the profiles of the 1D-model, which are used to initialize the 3D-model, in the standard profile data output of the 3D-model (which is controlled by parameter \texttt{\textcolor{blue}{data\_output\_pr}}) by adding a \texttt{'\#'} sign to the respective output quantity, e.g. \texttt{\textcolor{blue}{data\_output\_pr} = '\#u'}.
           \vspace{0.5em}
            \item<3-> For the 1D-model, please set \texttt{\textcolor{blue}{mixing\_length\_1d} = 'blackadar'} and \texttt{\textcolor{blue}{dissipation\_1d} = 'detering'} in order to get a correct mean boundary layer wind profile. The default settings of these parameters would switch the turbulence parameterization of the 1D-model to the SGS-parameterization of the 3D-LES-model, which represents only the SGS-parts of turbulence. However, for this exercise the 1D-model has to parameterize all scales of turbulence (i.e. it should be used as a RANS-model).
        \end{itemize}

        \item<4-> \textbf{Stationary state:}
        \begin{itemize}
           \tiny
           \item<4-> You probably will find it difficult to get the mean flow to a stationary state (for the 1D-model as well as for the 3D-model. Can you identify the mechanism responsible for this? Try parameters \texttt{\textcolor{blue}{damp\_level\_1d}} (for the 1D-model) and \texttt{\textcolor{blue}{rayleigh\_damping\_factor}} (for the 3D-model; this is a \texttt{inipar}-parameter!) to overcome this problem.
           \vspace{0.5em}
           \item<5-> You can switch on a Galilei-transformation in order to save CPU-time (see parameter \texttt{\textcolor{blue}{galilei\_transformation}}).
        \end{itemize}

     \end{itemize}
 \end{frame}

% Folie 5
 \begin{frame}
    \frametitle{Hints (II)}
     \begin{itemize}
        \item<1-> \textbf{Spectra:}
        \begin{itemize}
           \scriptsize
           \item<2-> Output of spectra requires to switch on the spectra-package using \textbf{mrun}-option \texttt{-p}:\\
                     \texttt{mrun ... -p spectra -r \dq d3\# sp\# ...\dq}
           \vspace{0.5em}
           \item<3-> Spectra output is controlled by parameters \texttt{\textcolor{blue}{data\_output\_sp}}, \texttt{\textcolor{blue}{dt\_dosp}}, etc. These package-parameters have to be given     in a separate NAMELIST-block which has to follow the \texttt{d3par}-block:\\
                     \texttt{\&d3par end\_time = ... /}\\
                     \texttt{\&spectra\_par data\_output\_sp = ... /}\\
        \end{itemize}
     \end{itemize}
 \end{frame}

% Folie 6
\section{Results}
\subsection{Results}

% Folie 7
\begin{frame}
   \frametitle{Time series of TKE}
   \begin{center}
      \includegraphics[width=1.0\textwidth]{exercise_neutral_figures/ts.eps}
   \end{center}
\end{frame}

% Folie 8
\begin{frame}
   \frametitle{Vertical profiles of $\overline{w'u'}$, $\overline{w'v'}$}
   \begin{center}
      \includegraphics[width=0.50\textwidth]{exercise_neutral_figures/pr_wu.eps}
      \includegraphics[width=0.50\textwidth]{exercise_neutral_figures/pr_wv.eps}\\
   \end{center}
\end{frame}

% Folie 9
\begin{frame}
   \frametitle{Vertical profiles of $\overline{w'u'}$, $\overline{w'v'}$}
   \begin{center}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/pr_wu_sgs.eps}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/pr_wv_sgs.eps}\\
      \vspace{-0.3em}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/pr_wu_resolved.eps}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/pr_wv_resolved.eps}\\
   \end{center}
\end{frame}

% Folie 10
\begin{frame}
   \frametitle{Spectra of $u$, $v$ and $w$}
      \hspace{-1em}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/sp_u.eps}
      \hspace{-2em}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/sp_v.eps}
      \hspace{-2em}
      \includegraphics[width=0.36\textwidth]{exercise_neutral_figures/sp_w.eps}
\end{frame}

\end{document}