1 | % $Id: exercise_neutral.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{tabto} |
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11 | \usepackage{multimedia} |
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12 | \usepackage{hyperref} |
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13 | \newcommand{\event}[1]{\newcommand{\eventname}{#1}} |
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14 | \usepackage{xmpmulti} |
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15 | \usepackage{tikz} |
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16 | \usetikzlibrary{shapes,arrows,positioning} |
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17 | \usetikzlibrary{decorations.markings} %neues paket |
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18 | \usetikzlibrary{decorations.pathreplacing} %neues paket |
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19 | \def\Tiny{\fontsize{4pt}{4pt}\selectfont} |
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20 | \usepackage{amsmath} |
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21 | \usepackage{amssymb} |
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22 | \usepackage{multicol} |
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23 | \usepackage{pdfcomment} |
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24 | \usepackage{graphicx} |
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25 | \usepackage{listings} |
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26 | \lstset{showspaces=false,language=fortran,basicstyle= |
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27 | \ttfamily,showstringspaces=false,captionpos=b} |
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28 | |
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29 | \institute{Institute of Meteorology and Climatology, Leibniz UniversitÃ€t Hannover} |
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30 | \selectlanguage{english} |
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31 | \date{last update: \today} |
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32 | \event{PALM Seminar} |
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33 | \setbeamertemplate{navigation symbols}{} |
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34 | |
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35 | \setbeamertemplate{footline} |
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36 | { |
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37 | \begin{beamercolorbox}[rightskip=-0.1cm]& |
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38 | {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}} |
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39 | \end{beamercolorbox} |
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40 | \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex, |
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41 | leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot} |
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42 | {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber} |
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43 | \end{beamercolorbox} |
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44 | \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot} |
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45 | \end{beamercolorbox} |
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46 | } |
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47 | %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}} |
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48 | |
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49 | \title[Exercise 2: Neutrally Stratified Boundary Layer]{Exercise 2: Neutrally Stratified Boundary Layer} |
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50 | \author{PALM group} |
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51 | |
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52 | \setbeamersize{text margin left=.2cm,text margin right=.2cm} |
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53 | |
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54 | \begin{document} |
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55 | \footnotesize |
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56 | % Folie 1 |
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57 | \begin{frame} |
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58 | \titlepage |
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59 | \end{frame} |
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60 | |
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61 | \section{Exercise} |
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62 | \subsection{Exercise} |
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63 | |
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64 | % Folie 2 |
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65 | \begin{frame} |
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66 | \frametitle{Exercise 2: Neutrally Stratified Atmospheric Boundary Layer} |
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67 | \begin{itemize} |
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68 | \item A neutrally stratified atmospheric boundary layer shall be simulated. |
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69 | \item<2-> The flow shall be driven by a constant large-scale pressure gradient, i.e., a geostrophic wind. |
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70 | \item<3-> At the end of the simulation, turbulence as well as the mean flow should be in a stationary state. |
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71 | \end{itemize} |
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72 | \onslide<4->\textbf{Simulation features:} |
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73 | \begin{itemize} |
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74 | \item<4-> geostrophic wind: \tabto{3cm} $u_\mathrm{g} = \unit[5]{m\ s^{-1}}, v_\mathrm{g} = \unit[0]{m\ s^{-1}}$ |
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75 | \item<5-> initial velocity: \tabto{3cm} try constant velocity ($u = u_\mathrm{g}, v = v_\mathrm{g}$, everywhere)\\ |
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76 | \tabto{3cm} or a mean vertical profile created by the 1D-model |
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77 | \item<6-> roughness length: \tabto{3cm} $z_0 = \unit[0.1]{m}$ |
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78 | \end{itemize} |
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79 | \onslide<7->Please choose domain size, grid size and time to be simulated appropriately. |
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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 | \begin{itemize} |
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86 | \item<1-> How long do you have to simulate until turbulence / mean flow become stationary? |
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87 | \vspace{1em} |
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88 | \item<2-> How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like? |
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89 | \vspace{1em} |
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90 | \item<3-> Is it really a large-eddy simulation, i.e., are the subgrid-scale fluxes much smaller than the resolved-scale fluxes? |
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91 | \vspace{1em} |
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92 | \item<4-> How do the turbulence spectra of $u$, $v$, $w$ along $x$ and along $y$ look like?\\ |
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93 | Can you identify the inertial subrange? |
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94 | \end{itemize} |
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95 | \end{frame} |
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96 | |
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97 | % Folie 4 |
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98 | \begin{frame} |
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99 | \frametitle{Hints (I)} |
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100 | \begin{itemize} |
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101 | \item<1-> Please remember hints given for the previous exercise! |
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102 | \item<2-> \textbf{Initial profiles:} |
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103 | \begin{itemize} |
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104 | \tiny |
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105 | \item<3-> The 1D-model (\texttt{\textcolor{blue}{initializing\_actions} = 'set\_1d-model\_profiles'}) is mainly controlled by parameters \texttt{\textcolor{blue}{end\_time\_1d}} and \texttt{\textcolor{blue}{damp\_level\_1d}}. Please keep in mind that the profiles from the 1D-model should also be in a stationary state. |
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106 | \vspace{0.5em} |
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107 | \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'}. |
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108 | \vspace{0.5em} |
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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). |
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110 | \end{itemize} |
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111 | |
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112 | \item<4-> \textbf{Stationary state:} |
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113 | \begin{itemize} |
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114 | \tiny |
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115 | \item<4-> You probably will find it difficult to get the mean flow to a stationary state (for the 1D-model as well as for the 3D-model. Can you identify the mechanism responsible for this? Try parameters \texttt{\textcolor{blue}{damp\_level\_1d}} (for the 1D-model) and \texttt{\textcolor{blue}{rayleigh\_damping\_factor}} (for the 3D-model; this is a \texttt{inipar}-parameter!) to overcome this problem. |
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116 | \vspace{0.5em} |
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117 | \item<5-> You can switch on a Galilei-transformation in order to save CPU-time (see parameter \texttt{\textcolor{blue}{galilei\_transformation}}). |
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118 | \end{itemize} |
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119 | |
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120 | \end{itemize} |
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121 | \end{frame} |
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122 | |
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123 | % Folie 5 |
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124 | \begin{frame} |
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125 | \frametitle{Hints (II)} |
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126 | \begin{itemize} |
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127 | \item<1-> \textbf{Spectra:} |
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128 | \begin{itemize} |
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129 | \scriptsize |
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130 | \item<2-> Output of spectra requires to switch on the spectra-package using \textbf{mrun}-option \texttt{-p}:\\ |
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131 | \texttt{mrun ... -p spectra -r \dq d3\# sp\# ...\dq} |
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132 | \vspace{0.5em} |
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133 | \item<3-> Spectra output is controlled by parameters \texttt{\textcolor{blue}{data\_output\_sp}}, \texttt{\textcolor{blue}{dt\_dosp}}, etc. These package-parameters have to be given in a separate NAMELIST-block which has to follow the \texttt{d3par}-block:\\ |
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134 | \texttt{\&d3par end\_time = ... /}\\ |
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135 | \texttt{\&spectra\_par data\_output\_sp = ... /}\\ |
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136 | \end{itemize} |
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137 | \end{itemize} |
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138 | \end{frame} |
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139 | |
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140 | % Folie 6 |
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141 | \section{Results} |
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142 | \subsection{Results} |
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143 | |
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144 | % Folie 7 |
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145 | \begin{frame} |
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146 | \frametitle{Time series of TKE, umax and wmax} |
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147 | \begin{center} |
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148 | \includegraphics[width=0.62\textwidth]{exercise_neutral_figures/ts_tke_umax_wmax.eps} |
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149 | \end{center} |
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150 | \end{frame} |
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151 | |
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152 | % Folie 8 |
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153 | \begin{frame} |
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154 | \frametitle{Vertical profiles of $\overline{w}$, $\overline{wu}$, $\overline{wv}$} |
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155 | \begin{center} |
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156 | \includegraphics[width=1.0\textwidth]{exercise_neutral_figures/pr_w_wu_wv.eps} |
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157 | \end{center} |
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158 | \end{frame} |
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159 | |
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160 | % Folie 9 |
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161 | \begin{frame} |
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162 | \frametitle{Vertical profiles of $\overline{w'u'}$, $\overline{w'v'}$, |
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163 | $\overline{w``u''}$ and $\overline{w``v''}$} |
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164 | \begin{center} |
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165 | \includegraphics[width=0.55\textwidth]{exercise_neutral_figures/pr_wu_wv_sgs_res.eps} |
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166 | \end{center} |
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167 | \end{frame} |
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168 | |
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169 | % Folie 10 |
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170 | \begin{frame} |
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171 | \frametitle{Spectra of $u$, $v$ and $w$} |
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172 | \begin{center} |
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173 | \includegraphics[angle=90,width=0.7\textwidth]{exercise_neutral_figures/sp_u_v_w.eps} |
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174 | \end{center} |
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175 | \end{frame} |
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176 | |
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177 | |
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178 | \subsection{Answers} |
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179 | % Folie 11 |
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180 | \begin{frame} |
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181 | \frametitle{Answers to question I} |
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182 | \footnotesize |
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183 | How long do you have to simulate until turbulence / mean flow become stationary? |
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184 | \begin{itemize} |
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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. |
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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 |
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187 | affecting the air parcels due to the Coriolis force. This oscillation is damped with time. |
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188 | \item umax and wmax do not change much in time after the spin-up time of roughly 6~h. |
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189 | \end{itemize} |
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190 | \end{frame} |
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191 | |
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192 | % Folie 12 |
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193 | \begin{frame} |
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194 | \frametitle{Answers to question II} |
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195 | \footnotesize |
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196 | How do the horizontally and temporally averaged vertical velocity and momentum flux profiles look like? |
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197 | \begin{itemize} |
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198 | \item The profiles are shown in frame 7. The horizontally averaged vertical velocity is practically zero as the usage of incompressible |
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199 | equations together with cyclic boundary conditions (horizontal homogeneity) suggest. |
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200 | \item wu an wv decrease with height since friction decelerates the flow at the surface. Due to the turning of the wind vector |
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201 | with height (Ekman spiral), |
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202 | the meridional velocity component is non-zero evoking also a non-zero vertical momentum flux of the v-velocity component. |
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203 | \item The non-convergence of the single profiles can be attributed to the inertial oscillation. |
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204 | \end{itemize} |
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205 | \end{frame} |
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206 | |
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207 | % Folie 13 |
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208 | \begin{frame} |
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209 | \frametitle{Answers to question III} |
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210 | \footnotesize |
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211 | Is it really a large-eddy simulation? |
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212 | \begin{itemize} |
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213 | \item Frame 8 shows sub-grid and resolved momentum flux profiles. |
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214 | \item The simulation is an LES since resolved momentum fluxes are the dominant components to the total flux except for the near |
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215 | vicinity of the surface where the unresolved, sub-grid fluxes dominate. |
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216 | \end{itemize} |
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217 | \end{frame} |
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218 | |
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219 | |
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220 | % Folie 14 |
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221 | \begin{frame} |
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222 | \frametitle{Answers to question IV} |
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223 | \footnotesize |
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224 | Can you identify the inertial subrange? |
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225 | \begin{itemize} |
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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 |
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227 | on the ordinate of the plots in frame 9 is dimensionless. |
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228 | \item The spectra show a maximum spectral density for small wave numbers. Thus, the largest eddies contain the highest variance |
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229 | (or turbulence kinetic energy, TKE). For higher wave numbers the inertial subrange follows where the spectra follow a -2/3 |
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230 | slope in the plot (indicated by a black line). There, the variance follows the energy cascade where larger eddies break-up |
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231 | into smaller eddies. For the highest wave numbers, the spectra depart from the -2/3 slope indicating that dissipation takes place. |
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232 | \item The spectra also show that the production range is not well developed (very flat maxima). This suggests that the modeling domain |
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233 | might be too small to capture relevant larger scales. |
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234 | \end{itemize} |
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235 | \end{frame} |
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236 | |
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237 | \end{document} |
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