Changeset 1534 for palm/trunk/TUTORIAL/SOURCE/exercise_neutral.tex
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 Jan 27, 2015 9:12:08 AM (10 years ago)
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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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