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\documentclass[english, 10pt, aspectratio=169]{beamer}
\useoutertheme{infolines}
\usecolortheme{whale}
\usepackage{polyglossia}
\setmainlanguage{english}
\usepackage{inter}
\usepackage{unicode-math}
\setmathfont[mathrm=sym]{Fira Math}
\setmonofont[Ligatures=TeX]{Fira Code}
\usepackage{csquotes}
\usepackage{siunitx}
\usepackage[
backend=biber,
style=iso-authoryear,
sorting=nyt,
]{biblatex}
\bibliography{library}
\title[50T block displacement]{Analysis of the displacement of a large concrete block under an extreme wave.}
\author[Edgar P. Burkhart]{Edgar P. Burkhart \and Stéphane Abadie}
\institute[SIAME]{Université de Pau et des Pays de lAdour, E2S-UPPA, SIAME, France}
\date[2022]{2022}
\begin{document}
\maketitle
\begin{frame}
\frametitle{Contents}
\tableofcontents
\end{frame}
\section{Contexte}
\subsection{Block displacement}
\begin{frame}
\frametitle{Context}
\framesubtitle{Block displacement}
\begin{columns}
\column{.7\textwidth}
\begin{itemize}
\item \citetitle{cox2018extraordinary} \parencite{cox2018extraordinary}
\item \citetitle{shah2013coastal} \parencite{shah2013coastal}
\end{itemize}
\column{.3\textwidth}
\includegraphics[width=\textwidth]{fig/cox.png}
\includegraphics[width=\textwidth]{fig/shah.png}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Context}
\framesubtitle{Analytical equations of block displacement}
\begin{itemize}
\item \citetitle{nott2003waves} \parencite{nott2003waves}
\begin{equation}
u^2\geq\frac{2\left(\frac{\rho_s}{\rho_w}-1\right)ag}{C_d\frac{ac}{b^2}+C_l}
\end{equation}
\item \citetitle{nandasena2011reassessment} \parencite{nandasena2011reassessment}
\begin{equation}
u^2\geq\frac{2\left(\frac{\rho_s}{\rho_w}-1\right)ag\left(\cos\theta+\frac cb\sin\theta\right)}
{C_d\frac{c^2}{b^2}+C_l}
\end{equation}
\item \citetitle{weiss2015untangling} \parencite{weiss2015untangling}
\end{itemize}
\end{frame}
\subsection{28-02-2017 event}
\begin{frame}
\frametitle{Context}
\framesubtitle{February 28, 2017 event}
\begin{figure}
\centering
\includegraphics[width=.5\textwidth]{fig/artha.jpg}
\caption{\SI{50}{\tonne} concrete block displaced by a wave onto the crest of the Artha breakwater
($h=\SI{8}{\m}$).}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Context}
\framesubtitle{February 28, 2017 event}
\begin{columns}
\column{.6\textwidth}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/ts.pdf}
\caption{Free surface measured during the extreme wave identified on February 28, 2017 at 17:23 UTC
($H=\SI{13.9}{\m}$).}
\end{figure}
\column{.4\textwidth}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/out_orbitals.pdf}
\caption{Trajectory of the wave buoy during this particular wave.}
\end{figure}
\end{columns}
\end{frame}
\section{Results}
\subsection{Wavelet analysis}
\begin{frame}
\frametitle{Wavelet analysis}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/wavelet.pdf}
\caption{Normalized wavelet power spectrum of rogue waves on February 28, 2017.}
\end{figure}
\end{frame}
\subsection{1D SWASH model}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Reflection study}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/bathy.pdf}
\caption{Domain 1 studied with a SWASH model (real case).}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Reflection study}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/bathy_nb.pdf}
\caption{Domain 2 studied with a SWASH model (without breakwater).}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Reflection study}
\begin{itemize}
\item 1D model over 2 layers (instability with more layers)
\item Mesh with \SI{1}{\m} resolution
\item Spectral boundary condition with buoy spectrum
\item \SI{4}{\hour} model duration (around 1200 waves)
\item Model calibrated by \textcite{poncet2021characterization}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Reflection study}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/maxw.pdf}
\caption{Free surface calculated by swash with spectral boundary condition at the buoy location. The plot is
centered on the largest obtained wave.\newline {\itshape Case 1: Real bathymetry; Case 2: simplified bathymetry (no
breakwater).}}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Wave propagation from the buoy to the breakwater}
\begin{itemize}
\item 1D model over 4 layers (instability with more layers)
\item Mesh with \SI{1}{\m} resolution
\item Free surface elevation boundary condition with raw buoy data
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Wave propagation from the buoy to the breakwater}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/x.pdf}
\caption{Propagation of the studied wave from the buoy to the Artha breakwater.}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{1-dimensionnal SWASH model}
\framesubtitle{Wavelet analysis}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/wavelet_sw.pdf}
\caption{Wavelet analysis from free surface elevation computed by SWASH along the SWASH domain.}
\end{figure}
\end{frame}
\subsection{2Dv Olaflow model}
\begin{frame}
\frametitle{Olaflow model in 2 vertical dimensions}
\framesubtitle{Study of the hydrodynamic conditions on the breakwater armour}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/aw_t0.pdf}
\caption{Domain studied with a 2Dv Olaflow model.}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Olaflow model in 2 vertical dimensions}
\framesubtitle{Study of the hydrodynamic conditions on the breakwater armour}
\begin{itemize}
\item VOF model based on VARANS equations
\item 2Dv mesh with \SI{50}{\cm} resolution
\item $k-\omega$ SST turbulence model
\item Qualitative calibration using photographs
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Olaflow model in 2 vertical dimensions}
\framesubtitle{Study of the hydrodynamic conditions on the breakwater armour}
\begin{figure}
\centering
\includegraphics[scale=.75]{fig/U.pdf}
\caption{Flow velocity computed on the Artha breakwater ($x=\SI{-20}{\m}$); bottom: $z=\SI{5}{\m}$.}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Olaflow model in 2 vertical dimensions}
\framesubtitle{Study of the hydrodynamic conditions on the breakwater armour}
\begin{itemize}
\item Flow velocity computed with Olaflow:
\begin{equation}
U = \SI{14.5}{\m\per\s}
\end{equation}
\item Flow velocity calculated using \textcite{nandasena2011reassessment}:
\begin{equation}
U = \SI{19.4}{\m\per\s}
\end{equation}
\item \textcite{weiss2015untangling}: time dependency does matter.
\end{itemize}
\end{frame}
\section{Conclusion}
\begin{frame}
\frametitle{Conclusion}
\begin{itemize}
\item Flow velocity lower than \textcite{nandasena2011reassessment}, in accordance with \textcite{lodhi2020role}
\item Time dependency matters, in accordance with \textcite{weiss2015untangling}
\end{itemize}
\end{frame}
\appendix
\section{References}
\begin{frame}[allowframebreaks]
\frametitle{References}
\printbibliography
\end{frame}
\end{document}