1 | % $Id: exercise_cbl.tex 1649 2015-09-15 16:34:42Z knoop $ |
---|
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} |
---|
16 | \def\Tiny{\fontsize{4pt}{4pt}\selectfont} |
---|
17 | |
---|
18 | %---------- neue Pakete |
---|
19 | \usepackage{amsmath} |
---|
20 | \usepackage{amssymb} |
---|
21 | \usepackage{multicol} |
---|
22 | \usepackage{pdfcomment} |
---|
23 | |
---|
24 | |
---|
25 | \institute{Institute of Meteorology and Climatology, Leibniz UniversitÃ€t Hannover} |
---|
26 | \selectlanguage{english} |
---|
27 | \date{last update: \today} |
---|
28 | \event{PALM Seminar} |
---|
29 | \setbeamertemplate{navigation symbols}{} |
---|
30 | |
---|
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 | } |
---|
43 | %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}} |
---|
44 | |
---|
45 | \title[Exercise 1: Convection Between Plates]{Exercise 1: Convection Between Plates} |
---|
46 | \author{PALM group} |
---|
47 | |
---|
48 | \begin{document} |
---|
49 | |
---|
50 | % Folie 1 |
---|
51 | \begin{frame} |
---|
52 | \titlepage |
---|
53 | \end{frame} |
---|
54 | |
---|
55 | \section{Exercise} |
---|
56 | \subsection{Exercise} |
---|
57 | |
---|
58 | % Folie 2 |
---|
59 | \begin{frame} |
---|
60 | \frametitle{Exercise 1: Convection Between Plates} |
---|
61 | |
---|
62 | Please try to carry out a run with following initial and boundary conditions and create the required output. |
---|
63 | \begin{itemize} |
---|
64 | \scriptsize |
---|
65 | \item<2-> The simulation should represent a stationary convective boundary layer between two uniformly heated/cooled plates with zero mean flow. |
---|
66 | \item<3-> A free-slip condition for velocity shall be used at the bottom and top boundary. |
---|
67 | \item<4-> The sensible heat flux at the bottom and top boundary shall be constant throughout the simulation. |
---|
68 | \end{itemize} |
---|
69 | \onslide<5-> Simulation features: |
---|
70 | \begin{itemize} |
---|
71 | \scriptsize |
---|
72 | \item<6-> domain size: about $\unit[2000 \times 2000 \times 1000]{m^3}$ ($x$/$y$/$z$) |
---|
73 | \item<7-> grid size: $\unit[50]{m}$ equidistant |
---|
74 | \item<8-> simulated time: $\unit[3600]{s}$ |
---|
75 | \item<9-> surface heatflux: $\unit[0.1]{K\ m\ s^{-1}}$ |
---|
76 | \item<10-> heatflux at top: $\unit[0.1]{K\ m\ s^{-1}}$ |
---|
77 | \item<11-> initial temperature: $\unit[300]{K}$ everywhere |
---|
78 | \item<12-> initial velocity: zero everywhere |
---|
79 | \end{itemize} |
---|
80 | \end{frame} |
---|
81 | |
---|
82 | % Folie 3 |
---|
83 | \begin{frame} |
---|
84 | \frametitle{Questions to be Answered:} |
---|
85 | |
---|
86 | \begin{itemize} |
---|
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?) |
---|
88 | \item<2-> How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like? |
---|
89 | \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?) |
---|
90 | \item<4-> How do the total kinetic energy and the maximum velocity components change in time? Has the flow become stationary? |
---|
91 | \item<5-> Has the domain size and grid size been chosen appropriately? |
---|
92 | \end{itemize} |
---|
93 | |
---|
94 | \end{frame} |
---|
95 | |
---|
96 | % Folie 4 |
---|
97 | \begin{frame} |
---|
98 | \frametitle{Hints (I)} |
---|
99 | \scriptsize |
---|
100 | |
---|
101 | PALM parameter names are displayed by courier style, e.g. \textcolor{blue}{\texttt{end\_time}}.\\ |
---|
102 | |
---|
103 | \begin{itemize} |
---|
104 | \item<2-> Domain size |
---|
105 | \begin{itemize} |
---|
106 | \scriptsize |
---|
107 | \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}}. |
---|
108 | \end{itemize} |
---|
109 | |
---|
110 | \item<3-> Initial profiles |
---|
111 | \begin{itemize} |
---|
112 | \scriptsize |
---|
113 | \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. |
---|
114 | \end{itemize} |
---|
115 | |
---|
116 | \item<4-> Boundary conditions |
---|
117 | \begin{itemize} |
---|
118 | \scriptsize |
---|
119 | \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 donât allow to use a Prandtl-layer. |
---|
120 | \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}}. |
---|
121 | \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}}). |
---|
122 | \end{itemize} |
---|
123 | |
---|
124 | \item<7-> Simulation time: See parameter \textcolor{blue}{\texttt{end\_time}} |
---|
125 | |
---|
126 | \end{itemize} |
---|
127 | |
---|
128 | \end{frame} |
---|
129 | |
---|
130 | % Folie 5 |
---|
131 | \begin{frame} |
---|
132 | \frametitle{Hints (II)} |
---|
133 | \footnotesize |
---|
134 | |
---|
135 | Hints for data output. |
---|
136 | |
---|
137 | \begin{itemize} |
---|
138 | |
---|
139 | \item<2-> Variables |
---|
140 | \begin{itemize} |
---|
141 | \footnotesize |
---|
142 | \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). |
---|
143 | \end{itemize} |
---|
144 | |
---|
145 | \item<3-> Output intervals |
---|
146 | \begin{itemize} |
---|
147 | \footnotesize |
---|
148 | \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. |
---|
149 | \end{itemize} |
---|
150 | |
---|
151 | \item<4-> Time averaging |
---|
152 | \begin{itemize} |
---|
153 | \footnotesize |
---|
154 | \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}}. |
---|
155 | \end{itemize} |
---|
156 | |
---|
157 | \end{itemize} |
---|
158 | |
---|
159 | \end{frame} |
---|
160 | |
---|
161 | % Folie 6 |
---|
162 | \begin{frame} |
---|
163 | \frametitle{Further Hints} |
---|
164 | |
---|
165 | \onslide<2-> You will find some more detailed information to solve this exercise in the PALM-online-documentation under:\\ |
---|
166 | \ \\ |
---|
167 | \small\url{http://palm.muk.uni-hannover.de/trac/wiki/doc/app/examples/cbl}\\ |
---|
168 | \ \\ |
---|
169 | \normalsize (Attention: This documentation is for atmospheric convection with free upper lid.) |
---|
170 | \ \\ |
---|
171 | \ \\ |
---|
172 | \onslide<3-> \normalsize Please also visit\\ |
---|
173 | \ \\ |
---|
174 | \small\url{http://palm.muk.uni-hannover.de/trac/wiki/doc/app/netcdf}\\ |
---|
175 | \ \\ |
---|
176 | \normalsize where the complete PALM netCDF-data-output and the respective steering parameters are described. |
---|
177 | |
---|
178 | \end{frame} |
---|
179 | |
---|
180 | % Folie 7 |
---|
181 | \begin{frame} |
---|
182 | \frametitle{How to Start?} |
---|
183 | |
---|
184 | \begin{itemize} |
---|
185 | \item<2-> Create a data directory for a new run:\\ |
---|
186 | \quad \texttt{cd \~{}/palm/current\_version}\\ |
---|
187 | \quad \texttt{mkdir -p JOBS/uniform\_plates/INPUT} |
---|
188 | |
---|
189 | \item<3-> Create the parameter file and set the required parameters in\\ |
---|
190 | \quad \texttt{JOBS/uniform\_plates/INPUT/uniform\_plates\_p3d} |
---|
191 | |
---|
192 | \item<4-> Start the run with \texttt{mrun-command}\\ |
---|
193 | \quad \texttt{mrun -d uniform\_plates -h <hi> -K parallel ...}\\ |
---|
194 | and analyze the output files. |
---|
195 | |
---|
196 | \end{itemize} |
---|
197 | |
---|
198 | \ \\ |
---|
199 | |
---|
200 | \onslide<5-> \huge \centering \textcolor{blue}{Good Luck!} |
---|
201 | |
---|
202 | \end{frame} |
---|
203 | |
---|
204 | % Folie 8 |
---|
205 | \section{Results} |
---|
206 | \subsection{Results} |
---|
207 | |
---|
208 | \begin{frame} |
---|
209 | \frametitle{$xy$-cross sections (instantaneous at $t = \unit[3600]{s}$)} |
---|
210 | \begin{center} |
---|
211 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_100.eps} |
---|
212 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\ |
---|
213 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_750.eps} |
---|
214 | \end{center} |
---|
215 | \end{frame} |
---|
216 | |
---|
217 | % Folie 9 |
---|
218 | \begin{frame} |
---|
219 | \frametitle{$xz$-cross sections ($\unit[900]{s}$ average)} |
---|
220 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y250m.eps} |
---|
221 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y500m.eps}\\ |
---|
222 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y750m.eps} |
---|
223 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y1000m.eps} |
---|
224 | \end{frame} |
---|
225 | |
---|
226 | % Folie 10 |
---|
227 | \begin{frame} |
---|
228 | \frametitle{Vertical profiles} |
---|
229 | \begin{center} |
---|
230 | \includegraphics[angle=90,width=\textwidth]{exercise_cbl_figures/pr_pt.eps} |
---|
231 | \end{center} |
---|
232 | \end{frame} |
---|
233 | |
---|
234 | % Folie 11 |
---|
235 | \begin{frame} |
---|
236 | \frametitle{LES?} |
---|
237 | \begin{center} |
---|
238 | \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/pr_wpt_res_sgs.eps} |
---|
239 | \end{center} |
---|
240 | \end{frame} |
---|
241 | |
---|
242 | % Folie 12 |
---|
243 | \begin{frame} |
---|
244 | \frametitle{Time series (I)} |
---|
245 | \begin{center} |
---|
246 | \includegraphics[angle=90,width=1.0\textwidth]{exercise_cbl_figures/ts.eps} |
---|
247 | \end{center} |
---|
248 | \end{frame} |
---|
249 | |
---|
250 | % Folie 13 |
---|
251 | \begin{frame} |
---|
252 | \frametitle{Time series (II)} |
---|
253 | \begin{center} |
---|
254 | \includegraphics[angle=90,width=1.0\textwidth]{exercise_cbl_figures/ts2.eps} |
---|
255 | \end{center} |
---|
256 | \end{frame} |
---|
257 | |
---|
258 | |
---|
259 | \subsection{Answers} |
---|
260 | |
---|
261 | % Folie 14 |
---|
262 | \begin{frame} |
---|
263 | \frametitle{Answers to question I} |
---|
264 | \footnotesize |
---|
265 | How does the flow field look like after 60 minutes of simulated time? |
---|
266 | \begin{itemize} |
---|
267 | \item Useful output: for example instantaneous or time-averaged cross-sections of vertical velocity (frames 8--9). |
---|
268 | \item Flow field shows narrower updrafts and broader downdrafts, cellular pattern close to the heated/cooled plates in xy-sections of |
---|
269 | vertical velocity. |
---|
270 | \item The temporal mean of vertical velocity exhibits a circulation spanning the whole depth of the model domain. |
---|
271 | \end{itemize} |
---|
272 | \end{frame} |
---|
273 | |
---|
274 | % Folie 15 |
---|
275 | \begin{frame} |
---|
276 | \frametitle{Answers to question II} |
---|
277 | \footnotesize |
---|
278 | How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like? |
---|
279 | \begin{itemize} |
---|
280 | \item PALM standard profile output contains potential temperature and its vertical flux (shown in frame 10). |
---|
281 | \item Heating the lower plate and cooling the upper plate induces convection resulting in a well-mixed boundary layer where the |
---|
282 | potential temperature profile is constant with height. |
---|
283 | Temperature gradients remain at the domain boundaries since convective turbulence cannot remove them in the vicinity of the walls. |
---|
284 | \item In case of horizontal homogeneity, the temperature equation reduces to |
---|
285 | $\frac{\partial\theta}{\partial t}=-\frac{\partial\overline{w^{\prime}\theta^{\prime}}}{\partial z}$ in the present case. In a |
---|
286 | stationary state, it follows that $\frac{\partial\theta}{\partial t}= 0 $. Thus, the flux profile |
---|
287 | $\overline{w^{\prime}\theta^{\prime}}$ has to be constant with height -- as can be seen in frame 10. |
---|
288 | \item The total vertical heat flux is positive in the whole modeling domain indicating upward transport of warmer air |
---|
289 | parcels and downward transport of colder air parcels. |
---|
290 | \end{itemize} |
---|
291 | \end{frame} |
---|
292 | |
---|
293 | % Folie 16 |
---|
294 | \begin{frame} |
---|
295 | \frametitle{Answers to question III} |
---|
296 | \footnotesize |
---|
297 | Is it really a large-eddy simulation? Duration of averaging time? |
---|
298 | \begin{itemize} |
---|
299 | \item It is a large-eddy simulation because the sub-grid fluxes are negligibly small throughout the bulk of the mixed layer. There, the |
---|
300 | resolved flux is dominating the total flux indicating a well-resolved turbulent flow (frame 11). Sub-grid fluxes dominate close to |
---|
301 | the surface where the turbulent-eddies cannot be resolved. |
---|
302 | \item Typically, the averaging time should contain several large-eddy turnover times. The large-eddy turnover time can be defined as |
---|
303 | $\tau_{\mathrm{l}}=L/u$ where $L$ is the length-scale of the largest eddies in the flow and $u$ is their typical velocity scale. |
---|
304 | $\tau_{\mathrm{l}}$ can be interpreted as a typical time a turbulent eddy needs to traverse the modeling domain. In our case, |
---|
305 | $L$ is proportional to the domain height ($L\approx1000\,\mathrm{m}$) and $u$ is about $5\,\mathrm{ms^{-1}}$ (see time series of |
---|
306 | wmax on frame 12). Thus, $\tau_{\mathrm{l}}\approx200\,\mathrm{s}$. An averaging time of 600\,s chosen here |
---|
307 | is, thus, appropriate. |
---|
308 | \end{itemize} |
---|
309 | \end{frame} |
---|
310 | |
---|
311 | % Folie 17 |
---|
312 | \begin{frame} |
---|
313 | \frametitle{Answers to question IV} |
---|
314 | \footnotesize |
---|
315 | Has the flow become stationary? |
---|
316 | \begin{itemize} |
---|
317 | \item The time series of total kinetic energy E and the maximum velocities wmax, umax and vmax shown in frames 12-13 exhibit |
---|
318 | a spin-up phase of the model up to $t\approx2000\,\mathrm{s}$. During this initialization time, turbulence is triggered by |
---|
319 | random perturbations until turbulence starts to develop. |
---|
320 | \item A stationary state can be seen by means of an (almost) non-changing E with time. Constant maxima of the velocity |
---|
321 | components also indicate a stationary flow. |
---|
322 | \end{itemize} |
---|
323 | \end{frame} |
---|
324 | |
---|
325 | % Folie 18 |
---|
326 | \begin{frame} |
---|
327 | \frametitle{Answers to question V} |
---|
328 | \footnotesize |
---|
329 | Has the domain size and grid size been chosen appropriately? |
---|
330 | \begin{itemize} |
---|
331 | \item A domain size is generally appropriately chosen in case that several of the dominating flow structures fit into the modeling |
---|
332 | domain. From the xy-cross sections in frame 8 it becomes apparent that the typical hexagonal flow structures close to the |
---|
333 | surface can hardly be seen. The xz-cross sections in frame 9 also contain only |
---|
334 | one circulation. Thus, the domain size in our example seems to be too small to capture several energy-containing flow structures. |
---|
335 | \item The grid size should be chosen in the way that the dominating flow structures can be represented by at least several |
---|
336 | grid points (4-5). A grid spacing of 50~m as chosen in this exercise |
---|
337 | is appropriate since the flow structures exhibit horizontal length scales of about 1~km (see frame 8). |
---|
338 | \end{itemize} |
---|
339 | \end{frame} |
---|
340 | \end{document} |
---|