 ### Chapter 8: two figures

* Replace figure with energy and dissipation distributions (from
Leschnziner) with self-drawn, simpler alternative
* Add figure to illustrate instantaneous/average decomposition
parent 04cd3d27
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{06} \renewcommand{\lasteditday}{08} \renewcommand{\lasteditday}{11} \renewcommand{\numberofthischapter}{8} \renewcommand{\titleofthischapter}{\namechaptereight} ... ... @@ -107,11 +107,19 @@ \subsection{Average and fluctuation} For the purpose of quantifying turbulence, we distinguish, in a given flow, between the average velocity and the “turbulent part” of velocity. We thus decompose the velocity field into two components: one is the \vocab{average} flow $\left(\overline u, \overline v, \overline w\right)$, and the other the \vocab{instantaneous fluctuation} flow $\left(u', v', w'\right)$: For the purpose of quantifying turbulence, we distinguish, in a given flow, between the average velocity and the “turbulent part” of velocity, as illustrated in figure~\ref{fig_instantaneous_average}. We thus decompose the velocity field into two components: one is the \vocab{average} flow $\left(\overline u, \overline v, \overline w\right)$, and the other the \vocab{instantaneous fluctuation} flow $\left(u', v', w'\right)$: \begin{IEEEeqnarray}{rCl} u_i &\equiv& \overline u_i + u_i'\label{eq_def_average_u}\\ \overline{u_i'} &\equiv& 0 \end{IEEEeqnarray} \begin{figure}[ht] \begin{center} \includegraphics[width=0.9\textwidth]{instantaneous_average} \end{center} \supercaption{An example of the separation between instantaneous and average values, here for temperature. The instantaneous temperature $T$ is decomposed as the sum of the time-averaged temperature $\overline T$ (blue curve) and the fluctuation $T'$, whose average $\overline{T'}$ is zero (red curve).}{\wcfile{Average and instantaneous values.svg}{Figure} \cczero \oc} \label{fig_instantaneous_average} \end{figure} \subsection{Turbulence intensity} \coveredin{De Nevers \cite{denevers2004}} ... ... @@ -205,9 +213,9 @@ These two integral equations are only useful to understand the meaning of figure~\ref{fig_cascade_k_epsilon}, where the distribution of $k$ and $\epsilon$ across the scales of eddies is plotted. \begin{figure}[ht] \begin{center} \includegraphics[width=\textwidth]{spectra} \includegraphics[width=0.9\textwidth]{spectra} \end{center} \supercaption{Distribution of turbulent kinetic energy (left) and turbulent dissipation rate (right) in fully-developed homogeneous isotropic turbulence. In those diagrams, the $x$-axis displays the \vocab{wavelength} $\kappa \equiv 2\pi/l$, so that the small-scale eddies are on the right side, with large values of $\kappa$.}{Figure extracted from Leschziner~\cite{leschziner2015}} \supercaption{Distribution of turbulent kinetic energy (left) and of turbulent dissipation rate (right) in fully-developed homogeneous isotropic turbulence. The top diagrams are in linear scale, while the bottom diagrams are in logarithmic scale. In those diagrams, the horizontal axis displays $1/l$, so that the small-scale eddies are on the right side, and large-scale eddies are on the left side. \\Those energy and dissipation distributions are for the simplest occurrences of turbulence; their features (in particular, the curves’ slopes and the ratios between $\Lambda$ and $\epsilon$) are used as reference cases in the study of more complex cases.}{Figure \ccbysa by \olivier} \label{fig_cascade_k_epsilon} \end{figure} ... ...

61.7 KB 40.1 KB | W: | H:

51.2 KB | W: | H:  • 2-up
• Swipe
• Onion skin
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment