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\chapter{Introduction}
In February 2017, a \SI{50}{\tonne} concrete block was displaced by a wave onto
the Artha breakwater in Saint-Jean-de-Luz. This event was captured by a
photographer, and earlier work from \textcite{amir} allowed to extract the
conditions under which this event happened using field data along with
numerical modeling.
The goal of the present study is to establish a numerical model representing
the conditions under which this block displacement event happened at the scale
of the breakwater. The simulation will be performed using the olaFlow
\parencite{olaFlow} model in a three-dimensionnal setting.
This study presents several aspects that are crucial to consider in order to
obtain accurate results. The seastate that lead to the studied event is known
thanks to a wave buoy located in front of the breakwater \parencite{amir}.
However, in order to input an accurate incident wave into the numerical model,
it will be necessary to extract the incident and reflected waves from the raw
buoy data. Then, it will be necessary to accurately model the Artha breakwater,
especially regarding its porous character. Finally, the results of this
simulation will need to be compared to the literature on block displacement by
waves for validation.

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\chapter{Literature Review}
In this chapter, literature relevant to the present study will be reviewed.
\section{Separating incident and reflected components from wave buoy data}
The separation of incident and reflected waves is a crucial step in numerically
modeling a seastate. Using the raw data from a buoy as the input of a wave
model will lead to incorrect results in the domain as the flow velocity at the
boundary will not be correctly generated.
Several methods exist to extract incident and reflected components in measured
seastates,
and they can generally be categorised in two types of methods: array methods
and PUV methods \parencite{inch2016accurate}. Array methods rely on the use of
multiple measurement points of water level to extracted the incident and
reflected waves, while PUV methods use colocated pressure and velocity
measurements to separate incident and reflected components of the signal.
\subsection{Array methods}
\begin{itemize}
\item \cite{mansard1980measurement}: Presentation of least-square method to separate
incident and reflected spectra. Requires simultaneous measurement at 3
positions, on a line parallel to the direction of wave propagation.
\parencite{gaillard1980}
\item \cite{frigaard1995time}: Separate 2D wave field into waves propagating towards
and away from a structure, using 2 gauges. Method quite efficient, even with
small filters. SIRW Method, realtime.
\item \cite{baldock1999separation}: Starting from \textcite{frigaard1995time},
arbitrary 2D bathymetry using linear shoaling. Small error for large reflection
coefficients, larger for low reflection.
\item \cite{suh2001separation}: Technique to separate incident and reflected waves on
a known current.
\item \cite{inch2016accurate}: creation of a lookup table to correct noise-induced
bias in array methods.
\item \cite{andersen2017estimation}: estimation of incident and reflected components
for non-linear waves.
\item \cite{roge2019estimation}: extension to irregular waves.
\end{itemize}
\subsection{PUV methods}
\begin{itemize}
\item ?? \cite{guza1977resonant}: model of the surf zone as a standing wave combined
with a progressive wave. Accurate results of surface elevation and runup for
reflectivities over 0.3.
\item ?? \cite{guza1984}:
\item \cite{tatavarti1989incoming}: Decompose colocated random field
measurements of wave elevation and currenct velocity into incoming and
outgoing components. Less sensitive to noise.
\item \cite{kubota1990}: comparison between different wave theories:
quasi-nonlinear long-wave theory gave the best results.
\item \cite{walton1992}: application to beaches, possibility to have higher
reflected energy than incident energy.
\item \cite{hughes1993}: colocated horizontal and vertical velocities or
horizontal velocity and surface elevation. Validation for full reflection of
irregular non breaking waves.
\item \cite{huntley1999use}: principal component analysis technique to avoid
noise-induced bias.
\item \cite{sheremet2002observations}:
\end{itemize}
\section{Modeling wave impact on a breakwater}
\subsection{SPH models}
\subsection{VARANS models}
\section{Modeling block displacement}