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\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 l’Adour, 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}