Changeset 1534 for palm/trunk/TUTORIAL/SOURCE/exercise_cbl.tex

Timestamp:

Jan 27, 2015 9:12:08 AM (9 years ago)

Author:

heinze

Message:

Revision of exercise_cbl and exercise_neutral

File:

• palm/trunk/TUTORIAL/SOURCE/exercise_cbl.tex (modified) (8 diffs)

palm/trunk/TUTORIAL/SOURCE/exercise_cbl.tex

@@ -6 +6 @@
 \usepackage{ngerman}
 \usepackage{pgf}
-\usetheme{Dresden}
 \usepackage{subfigure}
 \usepackage{units}
@@ -15 +14 @@
 \usepackage{tikz}
 \usetikzlibrary{shapes,arrows,positioning}
-\usetikzlibrary{decorations.markings}             %neues paket
-\usetikzlibrary{decorations.pathreplacing}        %neues paket
 \def\Tiny{\fontsize{4pt}{4pt}\selectfont}
+
+%---------- neue Pakete
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{multicol}
 \usepackage{pdfcomment}
-\usepackage{graphicx}
-\usepackage{listings}
-\lstset{showspaces=false,language=fortran,basicstyle=
-        \ttfamily,showstringspaces=false,captionpos=b}
+
 
 \institute{Institute of Meteorology and Climatology, Leibniz UniversitÀt Hannover}
@@ -91 +87 @@
    \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<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?
@@ -126 +122 @@
       \end{itemize}     
       
-      \item<7-> Simulation time
-      \begin{itemize}
-         \scriptsize
-         \item[-]<7-> See parameter \textcolor{blue}{\texttt{end\_time}}.
-      \end{itemize}
+      \item<7-> Simulation time: See parameter \textcolor{blue}{\texttt{end\_time}}
       
    \end{itemize}
@@ -217 +209 @@
    \frametitle{$xy$-cross sections (instantaneous at $t = \unit[3600]{s}$)}
    \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}
+      \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_100.eps}
+      \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\
+      \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_750.eps}
    \end{center}
 \end{frame}
@@ -226 +218 @@
 \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}
+    \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y250m.eps}
+    \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y500m.eps}\\
+    \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y750m.eps}
+    \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y1000m.eps}
 \end{frame}
 
 % Folie 10
 \begin{frame}
-   \frametitle{Vertical profiles (I)}
+   \frametitle{Vertical profiles}
    \begin{center}
       \includegraphics[angle=90,width=\textwidth]{exercise_cbl_figures/pr_pt.eps}
@@ -246 +236 @@
    \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}
+      \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/pr_wpt_res_sgs.eps}
    \end{center}
 \end{frame}
@@ -266 +255 @@
    \end{center}
 \end{frame}
+
+
+\subsection{Answers}
+
+% Folie 14
+\begin{frame}
+   \frametitle{Answers to question I}
+   \footnotesize
+   How does the flow field look like after 60 minutes of simulated time?
+   \begin{itemize}
+    \item Useful output: for example instantaneous or time-averaged cross-sections of vertical velocity (frames 8--9).
+    \item Flow field shows narrower updrafts and broader downdrafts, cellular pattern close to the heated/cooled plates in xy-sections of 
+          vertical velocity.
+    \item The temporal mean of vertical velocity exhibits a circulation spanning the whole depth of the model domain.
+   \end{itemize}
+\end{frame}
+
+% Folie 15
+\begin{frame}
+   \frametitle{Answers to question II}
+   \footnotesize
+   How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like?
+   \begin{itemize}
+    \item PALM standard profile output contains potential temperature and its vertical flux (shown in frame 10). 
+    \item Heating the lower plate and cooling the upper plate induces convection resulting in a well-mixed boundary layer where the 
+          potential temperature profile is constant with height. 
+          Temperature gradients remain at the domain boundaries since convective turbulence cannot remove them in the vicinity of the walls. 
+    \item In case of horizontal homogeneity, the temperature equation reduces  to 
+          $\frac{\partial\theta}{\partial t}=-\frac{\partial\overline{w^{\prime}\theta^{\prime}}}{\partial z}$ in the present case. In a 
+          stationary state, it follows that $\frac{\partial\theta}{\partial t}= 0 $. Thus, the flux profile 
+          $\overline{w^{\prime}\theta^{\prime}}$ has to be constant with height -- as can be seen in frame 10.
+    \item The total vertical heat flux is positive in the whole modeling domain indicating upward transport of warmer air 
+          parcels and downward transport of colder air parcels. 
+   \end{itemize}
+\end{frame}
+
+% Folie 16
+\begin{frame}
+   \frametitle{Answers to question III}
+   \footnotesize
+   Is it really a large-eddy simulation? Duration of averaging time?
+   \begin{itemize}
+    \item It is a large-eddy simulation because the sub-grid fluxes are negligibly small throughout the bulk of the mixed layer. There, the 
+          resolved flux is dominating the total flux indicating a well-resolved turbulent flow (frame 11). Sub-grid fluxes dominate close to 
+          the surface where the turbulent-eddies cannot be resolved.
+    \item Typically, the averaging time should contain several large-eddy turnover times. The large-eddy turnover time can be defined as 
+          $\tau_{\mathrm{l}}=L/u$ where $L$ is the length-scale of the largest eddies in the flow and $u$ is their typical velocity scale. 
+          $\tau_{\mathrm{l}}$ can be interpreted as a typical time a turbulent eddy needs to traverse the modeling domain. In our case, 
+          $L$ is proportional to the domain height ($L\approx1000\,\mathrm{m}$) and $u$ is about $5\,\mathrm{ms^{-1}}$ (see time series of 
+          wmax on frame 12). Thus, $\tau_{\mathrm{l}}\approx200\,\mathrm{s}$. An averaging time of 600\,s chosen here 
+          is, thus, appropriate. 
+   \end{itemize}
+\end{frame}
+
+% Folie 17
+\begin{frame}
+   \frametitle{Answers to question IV}
+   \footnotesize
+   Has the flow become stationary?
+   \begin{itemize}
+    \item The time series of total kinetic energy E and the maximum velocities wmax, umax and vmax shown in frames 12-13 exhibit 
+          a spin-up phase of the model up to $t\approx2000\,\mathrm{s}$. During this initialization time, turbulence is triggered by 
+          random perturbations until turbulence starts to develop.
+    \item A stationary state can be seen by means of an (almost) non-changing E with time. Constant maxima of the velocity 
+          components also indicate a stationary flow. 
+   \end{itemize}
+\end{frame}
+
+% Folie 18
+\begin{frame}
+   \frametitle{Answers to question V}
+   \footnotesize
+   Has the domain size and grid size been chosen appropriately?
+   \begin{itemize}
+    \item A domain size is generally appropriately chosen in case that several of the dominating flow structures fit into the modeling 
+          domain. From the xy-cross sections in frame 8 it becomes apparent that the typical hexagonal flow structures close to the 
+          surface can hardly be seen. The xz-cross sections in frame 9 also contain only 
+          one circulation. Thus, the domain size in our example seems to be too small to capture several energy-containing flow structures.
+    \item The grid size should be chosen in the way that the dominating flow structures can be represented by at least several 
+          grid points (4-5). A grid spacing of 50~m as chosen in this exercise 
+          is appropriate since the flow structures exhibit horizontal length scales of about 1~km (see frame 8).
+   \end{itemize}
+\end{frame}
 \end{document}