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1%$Id: exercise_topography.tex 1541 2015-01-28 11:14:05Z hoffmann $
2\input{header_tmp.tex}
3%\input{../header_lectures.tex}
4
5\usepackage[utf8]{inputenc}
6\usepackage{ngerman}
7\usepackage{pgf}
8\usepackage{subfigure}
9\usepackage{units}
10\usepackage{multimedia}
11\usepackage{hyperref}
12\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
13\usepackage{xmpmulti}
14\usepackage{tikz}
15\usetikzlibrary{shapes,arrows,positioning,decorations.pathreplacing}
16\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
17
18%---------- neue Pakete
19\usepackage{amsmath}
20\usepackage{amssymb}
21\usepackage{multicol}
22\usepackage{pdfcomment}
23\usepackage{xcolor}
24
25\institute{Institute of Meteorology and Climatology, Leibniz UniversitÀt Hannover}
26\selectlanguage{english}
27\date{last update: \today}
28\event{PALM Seminar}
29\setbeamertemplate{navigation symbols}{}
30\setbeamersize{text margin left=.5cm,text margin right=.2cm}
31\setbeamertemplate{footline}
32  {%
33    \begin{beamercolorbox}[rightskip=-0.1cm]&
34     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
35    \end{beamercolorbox}
36    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
37      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
38      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
39    \end{beamercolorbox}%
40%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
41%    \end{beamercolorbox}
42  }%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.eps}}
43
44\title[Exercise - Topography]{Exercise - Topography}
45\author{PALM group}
46
47% Notes:
48% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
49% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
50\begin{document}
51% Folie 1
52\begin{frame}
53\titlepage
54\end{frame}
55
56\section{Exercise}
57\subsection{Exercise}
58
59% Folie 2
60\begin{frame}
61   \frametitle{Exercise}
62   Please carry out \textbf{two runs} with following conditions.
63   \begin{itemize}
64      \item<2->{Single cube}
65      \begin{itemize}
66         \item[1.)]{First run ''generic'' using {\tt topography = 'single\_building'}}
67         \item[2.)]{Second run ''raster'' using {\tt topography = 'read\_from\_file'}
68                   with ASCII file ...\_topo}
69      \end{itemize}
70      \item<3->{Neutral boundary layer in a channel}
71      \item<4->{Constant bulk velocity}
72      \item<5->{No Coriolis force}
73      \item<6->{Simulation features:}
74      \begin{itemize}
75         \item{domain size: (80 m)$^3$ (x/y/z)}
76         \item{grid size: 2 m equidistant}
77         \item{cube: size (40 m)$^3$, location centered in the domain center}
78         \item{simulated time: 7200 s}
79         \item{initial velocity: u = 1, v = 0 m/s}
80      \end{itemize}
81   \end{itemize}
82   \onslide<7->\textbf{Please use the same building (size, location) for both runs!}
83\end{frame}
84
85% Folie 3
86\begin{frame}
87   \frametitle{Questions to be Answered}
88   \small
89   \begin{enumerate}
90      \item<2->{Can you identify any interesting flow patterns around the cube and what do they tell us?}
91      \begin{itemize}
92         \item{What kind of output do you need to answer this?}
93      \end{itemize}
94      \item<3->{How do the horizontally and temporally averaged velocity and momentum flux profiles look like?}
95      \begin{itemize}
96         \item{How long should the averaging time interval be?}
97      \end{itemize}
98      \item<4->{Is it really a fully developed large-eddy simulation?}
99      \begin{itemize}
100         \item{Are the subgrid-scale fluxes much smaller than the resolved-scale fluxes?}
101         \item{How do the total kinetic energy and the maximum velocity components change
102               with time?}
103      \end{itemize}
104      \item{\onslide<5->\textbf{Final question:} Do the results of both runs agree?}
105   \end{enumerate}
106\end{frame}
107
108% Folie 4
109\begin{frame}
110   \frametitle{Hints (I)}
111   \scriptsize
112   \begin{itemize}
113      \item<2->{\textbf{Domain size}}
114      \begin{itemize}
115         \scriptsize
116         \item{Is controlled by grid size (\textbf{dx}, \textbf{dy}, \textbf{dz}) and number of grid points
117               (\textbf{nx}, \textbf{ny}, \textbf{nz}). Since the first grid point along one of the directions has
118               index 0, the total number of grid points used are \textbf{nx}+1, \textbf{ny}+1, \textbf{nz}+1.
119               The total domain size in case of cyclic horizontal boundary conditions is
120               (\textbf{nx}+1)$\cdot$\textbf{dx}, (\textbf{ny}+1)$\cdot$\textbf{dy}.}
121         \end{itemize}
122      \item<3->{\textbf{Initial profiles}}
123      \begin{itemize}
124         \scriptsize
125         \item{Constant with height. See parameter \textbf{initializing\_actions} for available
126               initialization methods. See \textbf{ug\_surface}, \textbf{vg\_surface} for initial values of
127               velocity.}
128      \end{itemize}
129      \item<4->{\textbf{Boundary conditions}}
130      \begin{itemize}
131         \scriptsize
132         \item{For channel boundary condition, see \textbf{bc\_uv\_t}.}
133      \end{itemize}
134      \item<5->{\textbf{Forcing}}
135      \begin{itemize}
136         \scriptsize
137         \item{For constant bulk velocity, see \textbf{conserve\_volume\_flow}.}
138         \item{For Coriolis force, see \textbf{omega}.}
139         \item{For neutral flow, see \textbf{neutral}.}
140      \end{itemize}
141      \item<6->{\textbf{Topography}}
142      \begin{itemize}
143         \scriptsize
144         \item{For generic topography, see \textbf{building\_height}, \textbf{building\_length\_x} and
145               \textbf{building\_length\_y}.}
146         \item{For raster topography, please use a text editor to manually create an
147               ASCII ''raster\_topo'' file that contains the same building.}
148      \end{itemize}     
149    \end{itemize}
150 \end{frame}
151
152% Folie 5
153\begin{frame}
154   \frametitle{Hints (II)}
155   \footnotesize
156   \begin{itemize}
157      \item<2->{\textbf{Simulation time}}
158      \begin{itemize} 
159         \footnotesize       
160         \item{See parameter \textbf{end\_time}.}
161      \end{itemize}
162      \item<3->{\textbf{Variables}}
163      \begin{itemize}
164         \footnotesize
165         \item{Output variables are chosen with parameters \textbf{data\_output} (3d-data or
166               2d-cross-sections) and \textbf{data\_output\_pr} (profiles).}
167         \item{Time series are activated using \textbf{dt\_dots}.}         
168      \end{itemize}
169      \item<4->{\textbf{Output intervals}}
170      \begin{itemize}
171         \footnotesize
172         \item{Output intervals are set with parameter \textbf{dt\_data\_output}. This parameter
173               affects all output (cross-sections, profiles, etc.). Individual temporal
174               intervals for the different output quantities can be assigned using
175               parameters \textbf{dt\_do3d}, \textbf{dt\_do2d\_xy}, \textbf{dt\_do2d\_xz}, \textbf{dt\_do2d\_yz}, \textbf{dt\_dopr},
176               etc. }
177      \end{itemize}
178      \item<5->{\textbf{Time averaging}}
179      \begin{itemize}
180         \footnotesize
181         \item{Time averaging is controlled with parameters \textbf{averaging\_interval},
182               \textbf{averaging\_interval\_pr}, \textbf{dt\_averaging\_input}, \textbf{dt\_averaging\_input\_pr}.}
183      \end{itemize}
184   \end{itemize}
185\end{frame}
186
187% Folie 6
188\begin{frame}
189   \frametitle{Further Hints}
190   \scriptsize
191   Please see under \\
192   \textbf{http://palm.muk.uni-hannover.de/wiki/doc/app/netcdf}  \\ 
193   \par\medskip 
194   where the complete PALM netCDF-data-output and the respective steering parameters are described.
195   \par\medskip
196   For topography, see \\
197   \textbf{http://palm.muk.uni-hannover.de/wiki/doc/app/inipar\#topo}\\
198   \par\medskip
199   and especially for raster topography, see also
200   \textbf{http://palm.muk.uni-hannover.de/wiki/doc/app/iofiles\#TOPOGRAPHY\_DATA} \\
201   \par\medskip
202   as well as the presentation ''Using topography (I)''.
203\end{frame}
204
205% Folie 7
206\begin{frame}
207   \frametitle{Proceeding}
208   Please proceed as follows:
209   \begin{itemize}
210      \item<2->[1.]{Please run with the ''generic'' topography case first.}
211      \item<3->[2.]{Check your results to answer all questions – except the final question.}
212      \item<4->[3.]{After this run has finished, use ncview, ncdump etc. to check the precise
213               location of the building (look at 2D array \textit{zusi} that is contained in 2D xy
214               cross-sections and 3D volume data).}
215      \item<5->[4.]{Use this information to manually create the ''raster\_topo'' file.}
216      \item<6->[5.]{Run the ''raster'' topography case.}
217      \item<7->[6.]{Compare both simulation results to answer the final question.}
218   \end{itemize} 
219\end{frame}
220
221% Folie 8
222\begin{frame}
223   \frametitle{How to Start?}
224   \footnotesize
225   \begin{itemize}
226      \item<2->{Create two \textbf{INPUT} directories for both new runs: \\
227            {\tt cd $\sim$/palm/current\_version} \\           
228            {\tt mkdir -p JOBS/generic/INPUT} \\
229            {\tt mkdir -p JOBS/raster/INPUT}} 
230      \item<3->{Create the parameter files and {\tt raster\_topo} file and set the required
231            parameters in \\
232            {\tt JOBS/generic/INPUT/generic\_p3d} \\
233            {\tt JOBS/raster/INPUT/raster\_p3d}}
234      \item<4->{Start the runs one by one with mrun-commands \\
235            {\tt mrun -d generic -K parallel ...} \\
236            {\tt mrun -d raster -K parallel ...}}
237      \item<5->{and analyze the output files in \\
238            {\tt JOBS/generic/OUTPUT} \\
239            {\tt JOBS/raster/OUTPUT}}
240   \end{itemize}
241\end{frame}
242
243\section{Results}
244\subsection{Results}
245
246% Folie 9
247\begin{frame}
248   \frametitle{Question 1: Flow patterns (I)}
249   \par\smallskip
250   \footnotesize
251   \textbf{Horizontal cross sections of 1-h averaged velocity components \textit{u} and \textit{v}}
252   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/u_xy.eps} \hspace{0.8cm}
253   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/v_xy.eps} 
254\end{frame}
255
256% Folie 10
257\begin{frame}
258   \frametitle{Question 1: Flow patterns (II)}
259   \par\smallskip
260   \footnotesize
261   \textbf{Horizontal and streamwise vertical cross sections of 1-h averaged \\ velocity component \textit{w}}
262   \par\smallskip
263   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/w_xy.eps} \hspace{0.8cm}
264   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/w_xz.eps} 
265\end{frame}
266
267% Folie 11
268\begin{frame}
269   \frametitle{Question 1: Flow patterns (III)}
270   \par\smallskip
271   \footnotesize
272   \textbf{Streamlines (1-h average) for the same cross sections as seen in Frame 10 \\ for the \textit{w}-velocity}
273   \par\smallskip
274   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/streamlines/streamlines_xy.eps} \hspace{0.8cm}
275   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/streamlines/streamlines_xz.eps} \hspace{0.8cm}
276\end{frame}
277
278
279% Folie 12
280\begin{frame}
281   \frametitle{Question 2: Velocity and momentum flux profiles}
282   \par\smallskip
283   \footnotesize
284   \textbf{Vertical profiles of 1-h and horizontally averaged \textit{u}-, \textit{v}- and \textit{w}-velocity}
285   \par\smallskip
286   \includegraphics[width=\textwidth]{exercise_topography_figures/profiles/profile_uvw.png}
287\end{frame}
288
289% Folie 13
290\begin{frame}
291   \frametitle{Question 2: Velocity and momentum flux profiles}
292   \par\smallskip
293   \footnotesize
294   \textbf{Vertical profiles of 1-h and horizontally averaged total turbulent momentum \\ fluxes $wu$ and $wv$}
295   \par\smallskip
296   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/profiles/wu_time_pr.eps} \hspace{0.8cm}
297   \includegraphics[width=0.45\textwidth]{exercise_topography_figures/profiles/wv_time_pr.eps}
298\end{frame}
299
300% Folie 14
301\begin{frame}
302   \frametitle{Question 3: LES? - Fluxes}
303   \par\smallskip
304   \footnotesize
305   \textbf{Vertical profiles of 1-h and horizontally averaged momentum fluxes: total ($wu$), resolved-scale ($w^{*}u^{*}$) and subgrid-scale ($w''u''$) fluxes}
306   \par\smallskip
307   \begin{center}
308      \includegraphics[width=0.6\textwidth]{exercise_topography_figures/profiles/wu_comp_pr.eps}
309   \end{center}   
310\end{frame}
311
312% Folie 15
313\begin{frame}
314   \frametitle{Question 3: LES? - Time Series (I)}
315   \par\smallskip
316   \footnotesize
317   \textbf{Total kinetic energy \textit{E} of the flow and maximum \textit{u}-velocity in the model domain}
318   \par\smallskip
319   \begin{center}
320      \includegraphics[width=0.95\textwidth]{exercise_topography_figures/timeseries/E_ts.eps} \\
321      \includegraphics[width=0.95\textwidth]{exercise_topography_figures/timeseries/umax_ts.eps} 
322   \end{center}
323\end{frame}
324
325% Folie 16
326\begin{frame}
327   \frametitle{Question 3: LES? - Time Series (II)}
328   \par\smallskip
329   \footnotesize
330   \textbf{Maximum \textit{v}- and \textit{w}-velocity in the model domain}
331   \par\smallskip
332   \begin{center}
333      \includegraphics[width=\textwidth]{exercise_topography_figures/timeseries/vmax_ts.eps} \\
334      \includegraphics[width=\textwidth]{exercise_topography_figures/timeseries/wmax_ts.eps}
335   \end{center}
336\end{frame}
337
338\subsection{Answers}
339
340% Folie 17
341\begin{frame}
342   \frametitle{Answer to question 1 (I)}
343   \footnotesize
344   \textbf{Can you identify any interesting flow patterns around the cube and what do they tell us?}
345   \par\smallskip
346   \footnotesize
347   The 1-h-averaged near-surface horizontal velocity components \textit{u} and \textit{v} show (see Frame 9):
348   \scriptsize
349   \begin{itemize}
350      \item{reversed streamwise flow in the gap between leeward and windward cube wall,}
351      \item{diverging spanwise flow in the gap with nearly same magnitude as reversed spanwise flow.}
352   \end{itemize}
353   \par\smallskip
354   \footnotesize
355   The \textit{w}-velocity fields complete the picture (see Frame 10), we see:
356   \scriptsize
357   \begin{itemize}
358      \item{descending mean flow near the windward cube wall,}
359      \item{ascending mean flow near the leeward cube wall.}
360   \end{itemize}
361\end{frame}
362
363% Folie 18
364\begin{frame}
365   \frametitle{Answer to question 1 (II)}
366   \footnotesize
367   \textbf{Can you identify any interesting flow patterns around the cube and what do they tell us?}
368   \par\smallskip
369   \footnotesize
370   Streamlines in Frame 11 show an overall view of the mean horizontal (left; near surface) and the mean streamwise-vertical (right; center of cube wall) flow:
371   \scriptsize
372   \begin{itemize}
373    \item{left: in the gap between leeward and windward cube wall, streamlines are directed in opposite direction to the prescribed flow direction, and they diverge in the spanwise direction,}
374    \item{left: starting at the corners of the leeward cube wall, these diverging streamlines converge with the streamlines of the flow forced around the side walls of the cube,}
375    \item{right: above the cube roof, the mean flow is horizontal and directed as prescribed,} 
376    \item{right: in the streamwise gap, we find a rotor-like vortex, explaining the mean downward motion in the largest part of the gap, the upward motion at the leeward cube wall, and the reversed streamwise flow, covering almost fully the gap dimensions.}
377   \end{itemize}
378   \par\smallskip
379   \footnotesize
380   \textbf{Note:} Flow patterns can change significantly when the size of the gaps between buildings changes (see e.g. Oke, T. R. \textit{Street Design and Urban Canopy Layer Climate}. Energy and Buildings, 11 (1988)).
381\end{frame}
382
383% Folie 19
384\begin{frame}
385   \frametitle{Answer to question 2 (I)}
386   \footnotesize
387   \textbf{How do the horizontally and temporally averaged velocity and momentum flux profiles look like?}
388   \par\smallskip
389   \footnotesize
390   Frame 12 shows 1-h and horizontally averaged vertical profiles of velocity components \textit{u}, \textit{v} and \textit{w}:
391   \scriptsize
392   \begin{itemize}
393      \item{\textit{u}: Channel flow causes zero velocity at bottom and top domain wall. Upper domain half: Velocities increase with distance from upper channel wall, peaks at around 60m, and decreases quickly closer towards cube top. Lower domain half: \textit{u} further decreases towards bottom channel wall, due to roughness of the wall, and \textit{u} is much smaller here than in upper domain half, due to presence of cube.}
394      \item{\textit{v}: In the horizontal average, \textit{v}-component is much smaller than \textit{u}, and it fluctuates around zero. Time average should be increased to further eliminate these fluctuations. Flow is forced by \textit{u}-component}, and cube does not induce significant \textit{v} in horizontal mean.
395      \item{\textit{w}: Zero above, small negative values below cube top. In fully developed LES with sufficient domain size and averaging, horizontally averaged \textit{w} profile should be zero.}
396   \end{itemize}
397\end{frame}
398
399% Folie 20
400\begin{frame}
401   \frametitle{Answer to question 2 (II)}
402   \footnotesize
403   \textbf{How do the horizontally and temporally averaged velocity and momentum flux profiles look like?}
404   \par\smallskip
405   \footnotesize
406   Frame 13 shows 1-h and horizontally averaged vertical profiles of \textit{u} and \textit{v} components of total turbulent vertical momentum flux, for two ouput times:
407   \scriptsize
408   \begin{itemize}
409      \item{\textit{wv} is one order of magnitude smaller than \textit{wu} (flow is forced with the \textit{u}-component), hence, the \textit{wv} profile is not smooth, it strongly fluctuates with heigt and time.}
410      \item{In contrast, the \textit{wu} profile is smooth and barely changes from one 1-h average to the next, indicating sufficient averaging time.}
411   \end{itemize}
412\end{frame}
413
414% Folie 21
415\begin{frame}
416   \frametitle{Answer to question 2 (III)}
417   \footnotesize
418   \textbf{How does the horizontally and temporally averaged momentum flux profile look like?}
419   \par\smallskip
420   \scriptsize
421   \begin{itemize}
422      \item{This \textit{wu} profile of channel flow around a cube strongly deviates from the typical \textit{wu profile} in a neutral obstacle-free atmospheric boundary layer (ABL). In the latter, \textit{wu} takes largest negative values at the surface and increases towards zero at the top the boundary layer. This means, the flow is decelerated everywhere within the ABL due to surface friction. In the cube-flow, the \textit{wu} profile can be split into three regions:}
423      \begin{itemize}
424       {\scriptsize
425         \item{z=40 to 80m: linear increase with height, i.e. the flow is decelerated in this part. Up to 65m, \textit{wu} is negative, i.e. the roughness of the cube top causes the deceleration. Above, \textit{wu} is positive, i.e. the flow is decelerated due to the no-slip boundary condition at the domain top.}
426         \item{z=15 to 40m: decreasing with height, i.e. the flow is accelerated here, which can be attributed to the above-cube flow.}
427         \item{z=0 to 15m: increasing with height, meaning flow deceleration, due to surface friction.}}
428      \end{itemize}
429   \end{itemize}
430   \par\bigskip
431   \scriptsize
432   \textbf{Note: Such momentum flux profiles (\textit{wu}) are typical for urban and vegetation canopy flows.}
433\end{frame}
434
435
436% Folie 22
437\begin{frame}
438   \frametitle{Answer to question 3}
439   \footnotesize
440   \textbf{Is it really a fully developed large-eddy simulation?}
441   \par\smallskip
442   \scriptsize
443   \begin{itemize}
444      \item{Frame 14: Except near the surface and at the domain top, subgrid-scale momentum flux \textit{w``u''} is one order of magnitude smaller than the resolved-scale counterpart \textit{w*u*}, hence we can conclude, that the  grid spacing is sufficiently small in order to resolve the energy-containing eddies within this neutral flow around a solid cube.}
445      \item{Frame 15: Timeseries of the kinetic energy \textit{E} and the maximum \textit{u} value in the flow indicate that two hours of simulation time are sufficient for the spin up of the model. Both quantities level out towards the end of the simulation.}
446      \item{Frame 16: The temporal evolution of maximum \textit{v} and \textit{w} values indicates that the flow shows turbulent features, since both components frequently change signs.}
447   \end{itemize}
448\end{frame}
449
450\end{document}
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