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Discussion, methods swash

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@ -110,3 +110,12 @@
year={2008},
publisher={Annual Reviews}
}
@article{lodhi2020,
title={The role of hydrodynamic impact force in subaerial boulder transport by tsunami—Experimental evidence and revision of boulder transport equation},
author={Lodhi, Hira A and Hasan, Haider and Nandasena, NAK},
journal={Sedimentary Geology},
volume={408},
pages={105745},
year={2020},
publisher={Elsevier}
}

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@ -2,6 +2,7 @@
\usepackage{polyglossia} \usepackage{authblk}
\usepackage[sfdefault]{inter}
\usepackage{graphicx}
\usepackage[hmargin=2.1cm, vmargin=2.97cm]{geometry}
\setmainlanguage{english}
@ -126,7 +127,7 @@ the crest increases, with a zone reaching 400m long in front of the wave where t
\centering
\includegraphics{fig/x.pdf}
\caption{Propagation of the wave supposed to be responsible for the block displacement; highlighted zone:
qualitatively estimated position of the wave crest.}\label{fig:swash_trans}
qualitatively estimated position of the wave front.}\label{fig:swash_trans}
\end{figure*}
\subsection{Wavelet analysis}
@ -162,7 +163,6 @@ exhibits a water level over 5m for over 40s.
\begin{figure*}
\centering
\includegraphics{fig/aw_t0.pdf}
\includegraphics{fig/U.pdf}
\caption{Horizontal flow velocity computed with the olaFlow model at x=-20m on the breakwater armor. The identified
wave reaches this point around t=175s.}\label{fig:U}
@ -197,6 +197,75 @@ infragravity waves.
\subsection{Wave transformation}
The SWASH model yields a strongly changing wave over the domain, highlighting the highly complex composition of this
wave. Although the peak of the amplitude of the wave is reduced as the wave propagates, the length of the wave is
highlighted by the results. At T+60s for instance, the water level is under 0m for 400m, and then over 0m for around
the same length, showing the main infragavity component of the studied wave.
The wavelet analysis conducted at several points along the domain (Figure~\ref{fig:wavelet_sw}) show that the energy of
the studied wave (slightly before t=1500s) initially displays a strong infragravity component. Energy is then
transfered from the infragravity band towards shorter waves, and back to the infragravity band. This behavior is quite
unexpected, and further investigations should be conducted to understand and validate those results.
\subsection{Hydrodynamic conditions on the breakwater}
The hydrodynamic conditions on the breakwater are the main focus of this study. Considering an initially submerged
block, analytical equations proposed by \textcite{nandasena2011} yield a minimal flow velocity that would lead to block
displacement by saltation of 19.4m/s. The results from the Olaflow model yield a maximal wave velocity during the
displacement of the 50T concrete block of 14.5m/s. The results from the model are 25\% lower than the analytical value.
Those results tend to confirm recent research by \textcite{lodhi2020}, where it was found that the block displacement
threshold tend to overestimate the minimal flow velocity needed for block movement, although further validation of the
model that is used would be needed to confirm those findings.
Additionally, the flow velocity that is reached during the identified wave is not the highest that is reached in the
model. Other shorter waves yield similar flow velocities on the breakwater, but in a smaller timeframe. The importance
of time dependency in studying block displacement would be in accordance with research from \textcite{weiss2015}, who
suggested that the use of time-dependent equations for block displacement would lead to a better understanding of the
phenomenon.
\section{Methods}
\subsection{SWASH models}
\subsubsection{Domain}
A 1750m long domain is constructed in order to study wave reflection and wave transformation over the bottom from the
wave buoy to the breakwater. Bathymetry with a resolution of around 1m was used for most of the domain. The breakwater
model used in the study is taken from \textcite{poncet2021}. A smoothed section is created and considered as a porous
media in the model.
A second domain is constructed for reflection analysis. The second model is the same as the first, excepted that the
breakwater is replaced by a smooth slope in order to remove the reflection generated by the structure.
The reflection analysis is conducted over 4h in order to generate a fair range of conditions. The wave transformation
study was conducted over a 1h timeframe in order to allow the model to reach steady-state before the studied wave was
generated.
\subsubsection{Model}
A non-linear non-hydrostatic shallow water model (SWASH, \cite{zijlema2011}) is used to model wave reflection and
transformation on the studied domain. The study is conducted using a layered one-dimensional model, that allows to
consider porous media in the domain.
The reflection analysis was conducted with 2 layers as to prevent model instability in overtopping conditions. The
study of wave transformation and the generation of boundary conditions for the Olaflow model is done with 4 layers.
\subsubsection{Porosity}
In the SWASH model, the porous breakwater armour is represented using macroscale porosity. The porosity parameters were
calibrated in \textcite{poncet2021}.
\subsubsection{Boundary conditions}
Two different sets of boundary conditions were used for both studies. In all cases, a sponge layer was added to the
shorewards boundary to prevent wave reflection on the boundary. In the reflection analysis, offshore conditions were
generated using the wave spectrum extracted from buoy data during the storm. The raw vertical surface elevation
measured by the wave buoy was used in a second part.
\begin{figure*}
\centering
\includegraphics{fig/aw_t0.pdf}
\caption{Domain studied with Olaflow. Initial configuration.}\label{fig:of}
\end{figure*}
\printbibliography
\end{document}