Changeset 1534 for palm/trunk/TUTORIAL


Ignore:
Timestamp:
Jan 27, 2015 9:12:08 AM (7 years ago)
Author:
heinze
Message:

Revision of exercise_cbl and exercise_neutral

Location:
palm/trunk/TUTORIAL/SOURCE
Files:
5 added
14 deleted
2 edited

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  • palm/trunk/TUTORIAL/SOURCE/exercise_cbl.tex

    r1515 r1534  
    66\usepackage{ngerman}
    77\usepackage{pgf}
    8 \usetheme{Dresden}
    98\usepackage{subfigure}
    109\usepackage{units}
     
    1514\usepackage{tikz}
    1615\usetikzlibrary{shapes,arrows,positioning}
    17 \usetikzlibrary{decorations.markings}             %neues paket
    18 \usetikzlibrary{decorations.pathreplacing}        %neues paket
    1916\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
     17
     18%---------- neue Pakete
    2019\usepackage{amsmath}
    2120\usepackage{amssymb}
    2221\usepackage{multicol}
    2322\usepackage{pdfcomment}
    24 \usepackage{graphicx}
    25 \usepackage{listings}
    26 \lstset{showspaces=false,language=fortran,basicstyle=
    27         \ttfamily,showstringspaces=false,captionpos=b}
     23
    2824
    2925\institute{Institute of Meteorology and Climatology, Leibniz UniversitÀt Hannover}
     
    9187   \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?)
    9288   \item<2-> How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like?
    93    \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?)
     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?)
    9490   \item<4-> How do the total kinetic energy and the maximum velocity components change in time? Has the flow become stationary?
    9591   \item<5-> Has the domain size and grid size been chosen appropriately?
     
    126122      \end{itemize}     
    127123     
    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}}
    133125     
    134126   \end{itemize}
     
    217209   \frametitle{$xy$-cross sections (instantaneous at $t = \unit[3600]{s}$)}
    218210   \begin{center}
    219       \includegraphics[width=0.42\textwidth]{exercise_cbl_figures/xy_w_100.eps}
    220       \includegraphics[width=0.42\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\
    221       \includegraphics[width=0.42\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}
    222214   \end{center}
    223215\end{frame}
     
    226218\begin{frame}
    227219   \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}
    234224\end{frame}
    235225
    236226% Folie 10
    237227\begin{frame}
    238    \frametitle{Vertical profiles (I)}
     228   \frametitle{Vertical profiles}
    239229   \begin{center}
    240230      \includegraphics[angle=90,width=\textwidth]{exercise_cbl_figures/pr_pt.eps}
     
    246236   \frametitle{LES?}
    247237   \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}
    250239   \end{center}
    251240\end{frame}
     
    266255   \end{center}
    267256\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}
    268340\end{document}
  • palm/trunk/TUTORIAL/SOURCE/exercise_neutral.tex

    r1515 r1534  
    6767   \begin{itemize}
    6868      \item A neutrally stratified atmospheric boundary layer shall be simulated.
    69       \item<2-> The flow shall be driven by a constant large-scale pressure gradient, i.e. a geostrophic wind.
     69      \item<2-> The flow shall be driven by a constant large-scale pressure gradient, i.e., a geostrophic wind.
    7070      \item<3-> At the end of the simulation, turbulence as well as the mean flow should be in a stationary state.
    7171   \end{itemize}
     
    8888       \item<2-> How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like?
    8989       \vspace{1em}
    90        \item<3-> Is it really a large-eddy simulation, i.e. are the subgrid-scale fluxes much smaller than the resolved-scale fluxes?
     90       \item<3-> Is it really a large-eddy simulation, i.e., are the subgrid-scale fluxes much smaller than the resolved-scale fluxes?
    9191       \vspace{1em}
    9292       \item<4-> How do the turbulence spectra of $u$, $v$, $w$ along $x$ and along $y$ look like?\\
     
    107107            \item<3-> Output of vertical profile data generated by the 1D-model is controlled by parameter \texttt{\textcolor{blue}{dt\_pr\_1d}}. It is in ASCII-format and it is written into a separate file. You can include the profiles of the 1D-model, which are used to initialize the 3D-model, in the standard profile data output of the 3D-model (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'}.
    108108           \vspace{0.5em}
    109             \item<3-> For the 1D-model, 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 1D-model to the SGS-parameterization of the 3D-LES-model, which represents only the SGS-parts of turbulence. However, for this exercise the 1D-model has to parameterize all scales of turbulence (i.e. it should be used as a RANS-model).
     109            \item<3-> For the 1D-model, 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 1D-model to the SGS-parameterization of the 3D-LES-model, which represents only the SGS-parts of turbulence. However, for this exercise the 1D-model has to parameterize all scales of turbulence (i.e., it should be used as a RANS-model).
    110110        \end{itemize}
    111111
     
    144144% Folie 7
    145145\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}
    149149   \end{center}
    150150\end{frame}
     
    152152% Folie 8
    153153\begin{frame}
    154    \frametitle{Vertical profiles of $\overline{wu}$, $\overline{wv}$}
    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}
    157157   \end{center}
    158158\end{frame}
     
    163163               $\overline{w``u''}$ and $\overline{w``v''}$}
    164164   \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}
    167166   \end{center}
    168167\end{frame}
     
    170169% Folie 10
    171170\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}
    176179% Folie 11
    177180\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 spin-up 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 non-zero evoking also a non-zero vertical momentum flux of the v-velocity component.
     203    \item The non-convergence 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 large-eddy simulation?
     212   \begin{itemize}
     213    \item Frame 8 shows sub-grid 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, sub-grid 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 break-up
     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}
    182235\end{frame}
    183236
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