1 | % $Id: exercise_cbl.tex 1534 2015-01-27 09:12:08Z heinze $ |
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2 | \input{header_tmp.tex} |
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3 | %\input{../header_lectures.tex} |
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4 | |
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5 | \usepackage[utf8]{inputenc} |
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6 | \usepackage{ngerman} |
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7 | \usepackage{pgf} |
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8 | \usepackage{subfigure} |
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9 | \usepackage{units} |
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10 | \usepackage{multimedia} |
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11 | \usepackage{hyperref} |
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12 | \newcommand{\event}[1]{\newcommand{\eventname}{#1}} |
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13 | \usepackage{xmpmulti} |
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14 | \usepackage{tikz} |
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15 | \usetikzlibrary{shapes,arrows,positioning} |
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16 | \def\Tiny{\fontsize{4pt}{4pt}\selectfont} |
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17 | |
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18 | %---------- neue Pakete |
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19 | \usepackage{amsmath} |
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20 | \usepackage{amssymb} |
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21 | \usepackage{multicol} |
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22 | \usepackage{pdfcomment} |
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23 | |
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24 | |
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25 | \institute{Institute of Meteorology and Climatology, Leibniz UniversitÃ€t Hannover} |
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26 | \selectlanguage{english} |
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27 | \date{last update: \today} |
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28 | \event{PALM Seminar} |
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29 | \setbeamertemplate{navigation symbols}{} |
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30 | |
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31 | \setbeamertemplate{footline} |
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32 | { |
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33 | \begin{beamercolorbox}[rightskip=-0.1cm]& |
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34 | {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}} |
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35 | \end{beamercolorbox} |
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36 | \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex, |
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37 | leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot} |
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38 | {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber} |
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39 | \end{beamercolorbox} |
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40 | \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot} |
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41 | \end{beamercolorbox} |
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42 | } |
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43 | %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}} |
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44 | |
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45 | \title[Exercise 1: Convection Between Plates]{Exercise 1: Convection Between Plates} |
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46 | \author{PALM group} |
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47 | |
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48 | \begin{document} |
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49 | |
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50 | % Folie 1 |
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51 | \begin{frame} |
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52 | \titlepage |
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53 | \end{frame} |
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54 | |
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55 | \section{Exercise} |
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56 | \subsection{Exercise} |
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57 | |
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58 | % Folie 2 |
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59 | \begin{frame} |
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60 | \frametitle{Exercise 1: Convection Between Plates} |
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61 | |
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62 | Please try to carry out a run with following initial and boundary conditions and create the required output. |
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63 | \begin{itemize} |
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64 | \scriptsize |
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65 | \item<2-> The simulation should represent a stationary convective boundary layer between two uniformly heated/cooled plates with zero mean flow. |
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66 | \item<3-> A free-slip condition for velocity shall be used at the bottom and top boundary. |
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67 | \item<4-> The sensible heat flux at the bottom and top boundary shall be constant throughout the simulation. |
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68 | \end{itemize} |
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69 | \onslide<5-> Simulation features: |
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70 | \begin{itemize} |
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71 | \scriptsize |
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72 | \item<6-> domain size: about $\unit[2000 \times 2000 \times 1000]{m^3}$ ($x$/$y$/$z$) |
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73 | \item<7-> grid size: $\unit[50]{m}$ equidistant |
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74 | \item<8-> simulated time: $\unit[3600]{s}$ |
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75 | \item<9-> surface heatflux: $\unit[0.1]{K\ m\ s^{-1}}$ |
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76 | \item<10-> heatflux at top: $\unit[0.1]{K\ m\ s^{-1}}$ |
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77 | \item<11-> initial temperature: $\unit[300]{K}$ everywhere |
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78 | \item<12-> initial velocity: zero everywhere |
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79 | \end{itemize} |
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80 | \end{frame} |
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81 | |
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82 | % Folie 3 |
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83 | \begin{frame} |
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84 | \frametitle{Questions to be Answered:} |
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85 | |
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86 | \begin{itemize} |
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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?) |
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88 | \item<2-> How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like? |
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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?) |
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90 | \item<4-> How do the total kinetic energy and the maximum velocity components change in time? Has the flow become stationary? |
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91 | \item<5-> Has the domain size and grid size been chosen appropriately? |
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92 | \end{itemize} |
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93 | |
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94 | \end{frame} |
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95 | |
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96 | % Folie 4 |
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97 | \begin{frame} |
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98 | \frametitle{Hints (I)} |
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99 | \scriptsize |
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100 | |
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101 | PALM parameter names are displayed by courier style, e.g. \textcolor{blue}{\texttt{end\_time}}.\\ |
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102 | |
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103 | \begin{itemize} |
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104 | \item<2-> Domain size |
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105 | \begin{itemize} |
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106 | \scriptsize |
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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}}. |
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108 | \end{itemize} |
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109 | |
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110 | \item<3-> Initial profiles |
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111 | \begin{itemize} |
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112 | \scriptsize |
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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. |
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114 | \end{itemize} |
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115 | |
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116 | \item<4-> Boundary conditions |
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117 | \begin{itemize} |
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118 | \scriptsize |
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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. |
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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}}. |
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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}}). |
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122 | \end{itemize} |
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123 | |
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124 | \item<7-> Simulation time: See parameter \textcolor{blue}{\texttt{end\_time}} |
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125 | |
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126 | \end{itemize} |
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127 | |
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128 | \end{frame} |
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129 | |
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130 | % Folie 5 |
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131 | \begin{frame} |
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132 | \frametitle{Hints (II)} |
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133 | \footnotesize |
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134 | |
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135 | Hints for data output. |
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136 | |
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137 | \begin{itemize} |
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138 | |
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139 | \item<2-> Variables |
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140 | \begin{itemize} |
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141 | \footnotesize |
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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). |
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143 | \end{itemize} |
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144 | |
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145 | \item<3-> Output intervals |
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146 | \begin{itemize} |
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147 | \footnotesize |
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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. |
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149 | \end{itemize} |
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150 | |
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151 | \item<4-> Time averaging |
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152 | \begin{itemize} |
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153 | \footnotesize |
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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}}. |
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155 | \end{itemize} |
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156 | |
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157 | \end{itemize} |
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158 | |
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159 | \end{frame} |
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160 | |
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161 | % Folie 6 |
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162 | \begin{frame} |
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163 | \frametitle{Further Hints} |
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164 | |
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165 | \onslide<2-> You will find some more detailed information to solve this exercise in the PALM-online-documentation under:\\ |
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166 | \ \\ |
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167 | \small\url{http://palm.muk.uni-hannover.de/wiki/doc/app/examples/cbl}\\ |
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168 | \ \\ |
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169 | \normalsize (Attention: This documentation is for atmospheric convection with free upper lid.) |
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170 | \ \\ |
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171 | \ \\ |
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172 | \onslide<3-> \normalsize Please also visit\\ |
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173 | \ \\ |
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174 | \small\url{http://palm.muk.uni-hannover.de/wiki/doc/app/netcdf}\\ |
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175 | \ \\ |
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176 | \normalsize where the complete PALM netCDF-data-output and the respective steering parameters are described. |
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177 | |
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178 | \end{frame} |
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179 | |
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180 | % Folie 7 |
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181 | \begin{frame} |
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182 | \frametitle{How to Start?} |
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183 | |
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184 | \begin{itemize} |
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185 | \item<2-> Create a data directory for a new run:\\ |
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186 | \quad \texttt{cd \~{}/palm/current\_version}\\ |
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187 | \quad \texttt{mkdir -p JOBS/uniform\_plates/INPUT} |
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188 | |
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189 | \item<3-> Create the parameter file and set the required parameters in\\ |
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190 | \quad \texttt{JOBS/uniform\_plates/INPUT/uniform\_plates\_p3d} |
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191 | |
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192 | \item<4-> Start the run with \texttt{mrun-command}\\ |
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193 | \quad \texttt{mrun -d uniform\_plates -h <hi> -K parallel ...}\\ |
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194 | and analyze the output files. |
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195 | |
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196 | \end{itemize} |
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197 | |
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198 | \ \\ |
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199 | |
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200 | \onslide<5-> \huge \centering \textcolor{blue}{Good Luck!} |
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201 | |
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202 | \end{frame} |
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203 | |
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204 | % Folie 8 |
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205 | \section{Results} |
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206 | \subsection{Results} |
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207 | |
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208 | \begin{frame} |
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209 | \frametitle{$xy$-cross sections (instantaneous at $t = \unit[3600]{s}$)} |
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210 | \begin{center} |
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211 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_100.eps} |
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212 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_500.eps}\\ |
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213 | \includegraphics[width=0.4\textwidth]{exercise_cbl_figures/xy_w_750.eps} |
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214 | \end{center} |
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215 | \end{frame} |
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216 | |
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217 | % Folie 9 |
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218 | \begin{frame} |
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219 | \frametitle{$xz$-cross sections ($\unit[900]{s}$ average)} |
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220 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y250m.eps} |
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221 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y500m.eps}\\ |
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222 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y750m.eps} |
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223 | \includegraphics[width=0.52\textwidth]{exercise_cbl_figures/xz_w_y1000m.eps} |
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224 | \end{frame} |
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225 | |
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226 | % Folie 10 |
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227 | \begin{frame} |
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228 | \frametitle{Vertical profiles} |
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229 | \begin{center} |
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230 | \includegraphics[angle=90,width=\textwidth]{exercise_cbl_figures/pr_pt.eps} |
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231 | \end{center} |
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232 | \end{frame} |
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233 | |
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234 | % Folie 11 |
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235 | \begin{frame} |
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236 | \frametitle{LES?} |
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237 | \begin{center} |
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238 | \includegraphics[width=1.0\textwidth]{exercise_cbl_figures/pr_wpt_res_sgs.eps} |
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239 | \end{center} |
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240 | \end{frame} |
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241 | |
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242 | % Folie 12 |
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243 | \begin{frame} |
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244 | \frametitle{Time series (I)} |
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245 | \begin{center} |
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246 | \includegraphics[angle=90,width=1.0\textwidth]{exercise_cbl_figures/ts.eps} |
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247 | \end{center} |
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248 | \end{frame} |
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249 | |
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250 | % Folie 13 |
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251 | \begin{frame} |
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252 | \frametitle{Time series (II)} |
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253 | \begin{center} |
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254 | \includegraphics[angle=90,width=1.0\textwidth]{exercise_cbl_figures/ts2.eps} |
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255 | \end{center} |
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256 | \end{frame} |
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257 | |
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258 | |
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259 | \subsection{Answers} |
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260 | |
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261 | % Folie 14 |
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262 | \begin{frame} |
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263 | \frametitle{Answers to question I} |
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264 | \footnotesize |
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265 | How does the flow field look like after 60 minutes of simulated time? |
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266 | \begin{itemize} |
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267 | \item Useful output: for example instantaneous or time-averaged cross-sections of vertical velocity (frames 8--9). |
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268 | \item Flow field shows narrower updrafts and broader downdrafts, cellular pattern close to the heated/cooled plates in xy-sections of |
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269 | vertical velocity. |
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270 | \item The temporal mean of vertical velocity exhibits a circulation spanning the whole depth of the model domain. |
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271 | \end{itemize} |
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272 | \end{frame} |
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273 | |
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274 | % Folie 15 |
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275 | \begin{frame} |
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276 | \frametitle{Answers to question II} |
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277 | \footnotesize |
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278 | How do the horizontally and temporally averaged vertical temperature and heat flux profiles look like? |
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279 | \begin{itemize} |
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280 | \item PALM standard profile output contains potential temperature and its vertical flux (shown in frame 10). |
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281 | \item Heating the lower plate and cooling the upper plate induces convection resulting in a well-mixed boundary layer where the |
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282 | potential temperature profile is constant with height. |
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283 | Temperature gradients remain at the domain boundaries since convective turbulence cannot remove them in the vicinity of the walls. |
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284 | \item In case of horizontal homogeneity, the temperature equation reduces to |
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285 | $\frac{\partial\theta}{\partial t}=-\frac{\partial\overline{w^{\prime}\theta^{\prime}}}{\partial z}$ in the present case. In a |
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286 | stationary state, it follows that $\frac{\partial\theta}{\partial t}= 0 $. Thus, the flux profile |
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287 | $\overline{w^{\prime}\theta^{\prime}}$ has to be constant with height -- as can be seen in frame 10. |
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288 | \item The total vertical heat flux is positive in the whole modeling domain indicating upward transport of warmer air |
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289 | parcels and downward transport of colder air parcels. |
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290 | \end{itemize} |
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291 | \end{frame} |
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292 | |
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293 | % Folie 16 |
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294 | \begin{frame} |
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295 | \frametitle{Answers to question III} |
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296 | \footnotesize |
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297 | Is it really a large-eddy simulation? Duration of averaging time? |
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298 | \begin{itemize} |
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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 |
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300 | resolved flux is dominating the total flux indicating a well-resolved turbulent flow (frame 11). Sub-grid fluxes dominate close to |
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301 | the surface where the turbulent-eddies cannot be resolved. |
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302 | \item Typically, the averaging time should contain several large-eddy turnover times. The large-eddy turnover time can be defined as |
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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. |
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304 | $\tau_{\mathrm{l}}$ can be interpreted as a typical time a turbulent eddy needs to traverse the modeling domain. In our case, |
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305 | $L$ is proportional to the domain height ($L\approx1000\,\mathrm{m}$) and $u$ is about $5\,\mathrm{ms^{-1}}$ (see time series of |
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306 | wmax on frame 12). Thus, $\tau_{\mathrm{l}}\approx200\,\mathrm{s}$. An averaging time of 600\,s chosen here |
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307 | is, thus, appropriate. |
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308 | \end{itemize} |
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309 | \end{frame} |
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310 | |
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311 | % Folie 17 |
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312 | \begin{frame} |
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313 | \frametitle{Answers to question IV} |
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314 | \footnotesize |
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315 | Has the flow become stationary? |
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316 | \begin{itemize} |
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317 | \item The time series of total kinetic energy E and the maximum velocities wmax, umax and vmax shown in frames 12-13 exhibit |
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318 | a spin-up phase of the model up to $t\approx2000\,\mathrm{s}$. During this initialization time, turbulence is triggered by |
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319 | random perturbations until turbulence starts to develop. |
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320 | \item A stationary state can be seen by means of an (almost) non-changing E with time. Constant maxima of the velocity |
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321 | components also indicate a stationary flow. |
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322 | \end{itemize} |
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323 | \end{frame} |
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324 | |
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325 | % Folie 18 |
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326 | \begin{frame} |
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327 | \frametitle{Answers to question V} |
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328 | \footnotesize |
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329 | Has the domain size and grid size been chosen appropriately? |
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330 | \begin{itemize} |
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331 | \item A domain size is generally appropriately chosen in case that several of the dominating flow structures fit into the modeling |
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332 | domain. From the xy-cross sections in frame 8 it becomes apparent that the typical hexagonal flow structures close to the |
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333 | surface can hardly be seen. The xz-cross sections in frame 9 also contain only |
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334 | one circulation. Thus, the domain size in our example seems to be too small to capture several energy-containing flow structures. |
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335 | \item The grid size should be chosen in the way that the dominating flow structures can be represented by at least several |
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336 | grid points (4-5). A grid spacing of 50~m as chosen in this exercise |
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337 | is appropriate since the flow structures exhibit horizontal length scales of about 1~km (see frame 8). |
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338 | \end{itemize} |
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339 | \end{frame} |
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340 | \end{document} |
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