Changeset 1541 for palm/trunk/TUTORIAL/SOURCE/exercise_topography.tex
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- Jan 28, 2015 11:14:05 AM (10 years ago)
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palm/trunk/TUTORIAL/SOURCE/exercise_topography.tex
r1515 r1541 87 87 \frametitle{Questions to be Answered} 88 88 \small 89 \begin{ itemize}90 \item<2->{Can you identify flow convergence / divergence patterns near the cube?}89 \begin{enumerate} 90 \item<2->{Can you identify any interesting flow patterns around the cube and what do they tell us?} 91 91 \begin{itemize} 92 92 \item{What kind of output do you need to answer this?} 93 93 \end{itemize} 94 \item<3->{How does the horizontally and temporally averaged momentum flux profile look 95 like?} 94 \item<3->{How do the horizontally and temporally averaged velocity and momentum flux profiles look like?} 96 95 \begin{itemize} 97 96 \item{How long should the averaging time interval be?} 98 97 \end{itemize} 99 \item<4->{Is it really a large-eddy simulation?}98 \item<4->{Is it really a fully developed large-eddy simulation?} 100 99 \begin{itemize} 101 100 \item{Are the subgrid-scale fluxes much smaller than the resolved-scale fluxes?} … … 103 102 with time?} 104 103 \end{itemize} 105 \end{itemize} 106 \onslide<5->\textbf{Final question:} 107 \begin{itemize} 108 \item{Do the results of both runs agree?} 109 \end{itemize} 104 \item{\onslide<5->\textbf{Final question:} Do the results of both runs agree?} 105 \end{enumerate} 110 106 \end{frame} 111 107 … … 141 137 \item{For constant bulk velocity, see \textbf{conserve\_volume\_flow}.} 142 138 \item{For Coriolis force, see \textbf{omega}.} 139 \item{For neutral flow, see \textbf{neutral}.} 143 140 \end{itemize} 144 141 \item<6->{\textbf{Topography}} … … 214 211 \item<3->[2.]{Check your results to answer all questions â except the final question.} 215 212 \item<4->[3.]{After this run has finished, use ncview, ncdump etc. to check the precise 216 location of the building (look at 2D array zusithat is contained in 2D xy213 location of the building (look at 2D array \textit{zusi} that is contained in 2D xy 217 214 cross-sections and 3D volume data).} 218 215 \item<5->[4.]{Use this information to manually create the ''raster\_topo'' file.} … … 249 246 % Folie 9 250 247 \begin{frame} 251 \frametitle{Flow convergence / divergence (I)} 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}} 252 252 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/u_xy.eps} \hspace{0.8cm} 253 253 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/v_xy.eps} … … 256 256 % Folie 10 257 257 \begin{frame} 258 \frametitle{Flow convergence / divergence (II)} 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 259 263 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/w_xy.eps} \hspace{0.8cm} 260 264 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/cross_sections/w_xz.eps} … … 263 267 % Folie 11 264 268 \begin{frame} 265 \frametitle{Streamlines} 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 266 274 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/streamlines/streamlines_xy.eps} \hspace{0.8cm} 267 275 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/streamlines/streamlines_xz.eps} \hspace{0.8cm} … … 271 279 % Folie 12 272 280 \begin{frame} 273 \frametitle{Vertical profiles of $\overline{w'u'}$, $\overline{w'v'}$} 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 274 296 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/profiles/wu_time_pr.eps} \hspace{0.8cm} 275 297 \includegraphics[width=0.45\textwidth]{exercise_topography_figures/profiles/wv_time_pr.eps} 276 298 \end{frame} 277 299 278 % Folie 13 279 \begin{frame} 280 \frametitle{LES? - Fluxes} 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 281 307 \begin{center} 282 308 \includegraphics[width=0.6\textwidth]{exercise_topography_figures/profiles/wu_comp_pr.eps} … … 284 310 \end{frame} 285 311 286 % Folie 14 287 \begin{frame} 288 \frametitle{LES? - Time Series (I)} 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 289 319 \begin{center} 290 320 \includegraphics[width=0.95\textwidth]{exercise_topography_figures/timeseries/E_ts.eps} \\ … … 293 323 \end{frame} 294 324 295 % Folie 15 296 \begin{frame} 297 \frametitle{LES? - Time Series (II)} 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 298 332 \begin{center} 299 333 \includegraphics[width=\textwidth]{exercise_topography_figures/timeseries/vmax_ts.eps} \\ … … 302 336 \end{frame} 303 337 338 \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} 449 304 450 \end{document}
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