Changeset 1534 for palm/trunk/TUTORIAL
 Timestamp:
 Jan 27, 2015 9:12:08 AM (8 years ago)
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 palm/trunk/TUTORIAL/SOURCE
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palm/trunk/TUTORIAL/SOURCE/exercise_cbl.tex
r1515 r1534 6 6 \usepackage{ngerman} 7 7 \usepackage{pgf} 8 \usetheme{Dresden}9 8 \usepackage{subfigure} 10 9 \usepackage{units} … … 15 14 \usepackage{tikz} 16 15 \usetikzlibrary{shapes,arrows,positioning} 17 \usetikzlibrary{decorations.markings} %neues paket18 \usetikzlibrary{decorations.pathreplacing} %neues paket19 16 \def\Tiny{\fontsize{4pt}{4pt}\selectfont} 17 18 % neue Pakete 20 19 \usepackage{amsmath} 21 20 \usepackage{amssymb} 22 21 \usepackage{multicol} 23 22 \usepackage{pdfcomment} 24 \usepackage{graphicx} 25 \usepackage{listings} 26 \lstset{showspaces=false,language=fortran,basicstyle= 27 \ttfamily,showstringspaces=false,captionpos=b} 23 28 24 29 25 \institute{Institute of Meteorology and Climatology, Leibniz UniversitÃ€t 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?) 92 88 \item<2> How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like? 93 \item<3> Is it really a largeeddy simulation, i.e. are the subgridscale fluxes much smaller than the resolvedscale fluxes? (How long should the averaging time interval be?)89 \item<3> Is it really a largeeddy simulation, i.e., are the subgridscale fluxes much smaller than the resolvedscale fluxes? (How long should the averaging time interval be?) 94 90 \item<4> How do the total kinetic energy and the maximum velocity components change in time? Has the flow become stationary? 95 91 \item<5> Has the domain size and grid size been chosen appropriately? … … 126 122 \end{itemize} 127 123 128 \item<7> Simulation time 129 \begin{itemize} 130 \scriptsize 131 \item[]<7> See parameter \textcolor{blue}{\texttt{end\_time}}. 132 \end{itemize} 124 \item<7> Simulation time: See parameter \textcolor{blue}{\texttt{end\_time}} 133 125 134 126 \end{itemize} … … 217 209 \frametitle{$xy$cross sections (instantaneous at $t = \unit[3600]{s}$)} 218 210 \begin{center} 219 \includegraphics[width=0.4 2\textwidth]{exercise_cbl_figures/xy_w_100.eps}220 \includegraphics[width=0.4 2\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\221 \includegraphics[width=0.4 2\textwidth]{exercise_cbl_figures/xy_w_750.eps}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} 222 214 \end{center} 223 215 \end{frame} … … 226 218 \begin{frame} 227 219 \frametitle{$xz$cross sections ($\unit[900]{s}$ average)} 228 \begin{center} 229 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y250m.eps} 230 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y500m.eps}\\ 231 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y750m.eps} 232 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/xz_w_y1000m.eps} 233 \end{center} 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} 234 224 \end{frame} 235 225 236 226 % Folie 10 237 227 \begin{frame} 238 \frametitle{Vertical profiles (I)}228 \frametitle{Vertical profiles} 239 229 \begin{center} 240 230 \includegraphics[angle=90,width=\textwidth]{exercise_cbl_figures/pr_pt.eps} … … 246 236 \frametitle{LES?} 247 237 \begin{center} 248 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_wpt2.eps} 249 \includegraphics[width=0.55\textwidth]{exercise_cbl_figures/pr_wpt_resolved.eps} 238 \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/pr_wpt_res_sgs.eps} 250 239 \end{center} 251 240 \end{frame} … … 266 255 \end{center} 267 256 \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 timeaveraged crosssections of vertical velocity (frames 89). 268 \item Flow field shows narrower updrafts and broader downdrafts, cellular pattern close to the heated/cooled plates in xysections 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 wellmixed 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 largeeddy simulation? Duration of averaging time? 298 \begin{itemize} 299 \item It is a largeeddy simulation because the subgrid fluxes are negligibly small throughout the bulk of the mixed layer. There, the 300 resolved flux is dominating the total flux indicating a wellresolved turbulent flow (frame 11). Subgrid fluxes dominate close to 301 the surface where the turbulenteddies cannot be resolved. 302 \item Typically, the averaging time should contain several largeeddy turnover times. The largeeddy turnover time can be defined as 303 $\tau_{\mathrm{l}}=L/u$ where $L$ is the lengthscale 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 1213 exhibit 318 a spinup 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) nonchanging 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 xycross sections in frame 8 it becomes apparent that the typical hexagonal flow structures close to the 333 surface can hardly be seen. The xzcross 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 energycontaining 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 (45). 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} 268 340 \end{document} 
palm/trunk/TUTORIAL/SOURCE/exercise_neutral.tex
r1515 r1534 67 67 \begin{itemize} 68 68 \item A neutrally stratified atmospheric boundary layer shall be simulated. 69 \item<2> The flow shall be driven by a constant largescale pressure gradient, i.e. a geostrophic wind.69 \item<2> The flow shall be driven by a constant largescale pressure gradient, i.e., a geostrophic wind. 70 70 \item<3> At the end of the simulation, turbulence as well as the mean flow should be in a stationary state. 71 71 \end{itemize} … … 88 88 \item<2> How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like? 89 89 \vspace{1em} 90 \item<3> Is it really a largeeddy simulation, i.e. are the subgridscale fluxes much smaller than the resolvedscale fluxes?90 \item<3> Is it really a largeeddy simulation, i.e., are the subgridscale fluxes much smaller than the resolvedscale fluxes? 91 91 \vspace{1em} 92 92 \item<4> How do the turbulence spectra of $u$, $v$, $w$ along $x$ and along $y$ look like?\\ … … 107 107 \item<3> Output of vertical profile data generated by the 1Dmodel is controlled by parameter \texttt{\textcolor{blue}{dt\_pr\_1d}}. It is in ASCIIformat and it is written into a separate file. You can include the profiles of the 1Dmodel, which are used to initialize the 3Dmodel, in the standard profile data output of the 3Dmodel (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'}. 108 108 \vspace{0.5em} 109 \item<3> For the 1Dmodel, 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 1Dmodel to the SGSparameterization of the 3DLESmodel, which represents only the SGSparts of turbulence. However, for this exercise the 1Dmodel has to parameterize all scales of turbulence (i.e. it should be used as a RANSmodel).109 \item<3> For the 1Dmodel, 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 1Dmodel to the SGSparameterization of the 3DLESmodel, which represents only the SGSparts of turbulence. However, for this exercise the 1Dmodel has to parameterize all scales of turbulence (i.e., it should be used as a RANSmodel). 110 110 \end{itemize} 111 111 … … 144 144 % Folie 7 145 145 \begin{frame} 146 \frametitle{Time series of TKE }147 \begin{center} 148 \includegraphics[width= 1.0\textwidth]{exercise_neutral_figures/ts.eps}146 \frametitle{Time series of TKE, umax and wmax} 147 \begin{center} 148 \includegraphics[width=0.62\textwidth]{exercise_neutral_figures/ts_tke_umax_wmax.eps} 149 149 \end{center} 150 150 \end{frame} … … 152 152 % Folie 8 153 153 \begin{frame} 154 \frametitle{Vertical profiles of $\overline{w u}$, $\overline{wv}$}155 \begin{center} 156 \includegraphics[width= \textwidth]{exercise_neutral_figures/pr_wu.eps}\\154 \frametitle{Vertical profiles of $\overline{w}$, $\overline{wu}$, $\overline{wv}$} 155 \begin{center} 156 \includegraphics[width=1.0\textwidth]{exercise_neutral_figures/pr_w_wu_wv.eps} 157 157 \end{center} 158 158 \end{frame} … … 163 163 $\overline{w``u''}$ and $\overline{w``v''}$} 164 164 \begin{center} 165 \includegraphics[width=0.55\textwidth]{exercise_neutral_figures/pr_wu_sgs.eps}\\ 166 \includegraphics[width=0.55\textwidth]{exercise_neutral_figures/pr_wu_resolved.eps}\\ 165 \includegraphics[width=0.55\textwidth]{exercise_neutral_figures/pr_wu_wv_sgs_res.eps} 167 166 \end{center} 168 167 \end{frame} … … 170 169 % Folie 10 171 170 \begin{frame} 172 \frametitle{Spectra of $u$ and $v$} 173 \includegraphics[angle=90,width=1.0\textwidth]{exercise_neutral_figures/sp_u.eps} 174 \end{frame} 175 171 \frametitle{Spectra of $u$, $v$ and $w$} 172 \begin{center} 173 \includegraphics[angle=90,width=0.7\textwidth]{exercise_neutral_figures/sp_u_v_w.eps} 174 \end{center} 175 \end{frame} 176 177 178 \subsection{Answers} 176 179 % Folie 11 177 180 \begin{frame} 178 \frametitle{Spectra of $w$} 179 \begin{center} 180 \includegraphics[angle=90,width=0.6\textwidth]{exercise_neutral_figures/sp_w.eps} 181 \end{center} 181 \frametitle{Answers to question I} 182 \footnotesize 183 How long do you have to simulate until turbulence / mean flow become stationary? 184 \begin{itemize} 185 \item As can be seen in frame 6, a simulation time of about 48~h should at least be taken to obtain a roughly constant kinetic energy. 186 \item The time series of E shows an oscillation with a period of roughly 14~h. This can be attributed to the inertial oscillation 187 affecting the air parcels due to the Coriolis force. This oscillation is damped with time. 188 \item umax and wmax do not change much in time after the spinup time of roughly 6~h. 189 \end{itemize} 190 \end{frame} 191 192 % Folie 12 193 \begin{frame} 194 \frametitle{Answers to question II} 195 \footnotesize 196 How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like? 197 \begin{itemize} 198 \item The profiles are shown in frame 7. The horizontally averaged vertical velocity is practically zero as the usage of incompressible 199 equations together with cyclic boundary conditions (horizontal homogeneity) suggest. 200 \item wu an wv decrease with height since friction decelerates the flow at the surface. Due to the turning of the wind vector 201 with height (Ekman spiral), 202 the meridional velocity component is nonzero evoking also a nonzero vertical momentum flux of the vvelocity component. 203 \item The nonconvergence of the single profiles can be attributed to the inertial oscillation. 204 \end{itemize} 205 \end{frame} 206 207 % Folie 13 208 \begin{frame} 209 \frametitle{Answers to question III} 210 \footnotesize 211 Is it really a largeeddy simulation? 212 \begin{itemize} 213 \item Frame 8 shows subgrid and resolved momentum flux profiles. 214 \item The simulation is an LES since resolved momentum fluxes are the dominant components to the total flux except for the near 215 vicinity of the surface where the unresolved, subgrid fluxes dominate. 216 \end{itemize} 217 \end{frame} 218 219 220 % Folie 14 221 \begin{frame} 222 \frametitle{Answers to question IV} 223 \footnotesize 224 Can you identify the inertial subrange? 225 \begin{itemize} 226 \item In PALM, the spectral density is normalized by means of the variance and additionally multiplied by the wave number. Thus, the spectral density appearing 227 on the ordinate of the plots in frame 9 is dimensionless. 228 \item The spectra show a maximum spectral density for small wave numbers. Thus, the largest eddies contain the highest variance 229 (or turbulence kinetic energy, TKE). For higher wave numbers the inertial subrange follows where the spectra follow a 2/3 230 slope in the plot (indicated by a black line). There, the variance follows the energy cascade where larger eddies breakup 231 into smaller eddies. For the highest wave numbers, the spectra depart from the 2/3 slope indicating that dissipation takes place. 232 \item The spectra also show that the production range is not well developed (very flat maxima). This suggests that the modeling domain 233 might be too small to capture relevant larger scales. 234 \end{itemize} 182 235 \end{frame} 183 236
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