Merge branch 'nature'

nature/kalliope.conf

@@ -0,0 +1,4 @@
+[latex]
+engine=xelatex
+main=main.tex
+out=nature.pdf

nature/library.bib

@@ -0,0 +1,137 @@
+@misc{olaFlow,
+	author={Higuera, P.},
+	title={olaFlow: {CFD} for waves [{S}oftware].},
+	year=2017,
+	doi={10.5281/zenodo.1297013},
+	url={https://doi.org/10.5281/zenodo.1297013}
+}
+@report{parvin2020,
+	author={Amir Parvin},
+	title={Processes allowing large block displacement under wave action},
+	year={2020},
+}
+@article{cox2018,
+	title={Extraordinary boulder transport by storm waves (west of Ireland, winter 2013--2014), and criteria for analysing coastal boulder deposits},
+	author={Cox, R{\'o}nadh and Jahn, Kalle L and Watkins, Oona G and Cox, Peter},
+	journal={Earth-Science Reviews},
+	volume={177},
+	pages={623--636},
+	year={2018},
+	publisher={Elsevier}
+}
+@article{shah2013,
+	title={Coastal boulders in Martigues, French Mediterranean: evidence for extreme storm waves during the Little Ice Age},
+	author={Shah-Hosseini, M and Morhange, C and De Marco, A and Wante, J and Anthony, EJ and Sabatier, F and Mastronuzzi, G and Pignatelli, C and Piscitelli, A},
+	journal={Zeitschrift f{\"u}r Geomorphologie},
+	volume={57},
+	number={Suppl 4},
+	pages={181--199},
+	year={2013}
+}
+@article{nott1997,
+  title={Extremely high-energy wave deposits inside the Great Barrier Reef, Australia: determining the cause—tsunami or tropical cyclone},
+  author={Nott, Jonathan},
+  journal={Marine Geology},
+  volume={141},
+  number={1-4},
+  pages={193--207},
+  year={1997},
+  publisher={Elsevier}
+}
+@article{nott2003,
+	title={Waves, coastal boulder deposits and the importance of the pre-transport setting},
+	author={Nott, Jonathan},
+	journal={Earth and Planetary Science Letters},
+	volume={210},
+	number={1-2},
+	pages={269--276},
+	year={2003},
+	publisher={Elsevier}
+}
+@article{nandasena2011,
+	title={Reassessment of hydrodynamic equations: Minimum flow velocity to initiate boulder transport by high energy events (storms, tsunamis)},
+	author={Nandasena, NAK and Paris, Rapha{\"e}l and Tanaka, Norio},
+	journal={Marine Geology},
+	volume={281},
+	number={1-4},
+	pages={70--84},
+	year={2011},
+	publisher={Elsevier}
+}
+@article{weiss2015,
+	title={Untangling boulder dislodgement in storms and tsunamis: Is it possible with simple theories?},
+	author={Weiss, R and Diplas, P},
+	journal={Geochemistry, Geophysics, Geosystems},
+	volume={16},
+	number={3},
+	pages={890--898},
+	year={2015},
+	publisher={Wiley Online Library}
+}
+@article{zijlema2011,
+	title={SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters},
+	author={Zijlema, Marcel and Stelling, Guus and Smit, Pieter},
+	journal={Coastal Engineering},
+	volume={58},
+	number={10},
+	pages={992--1012},
+	year={2011},
+	publisher={Elsevier}
+}
+@article{higuera2015,
+	title={Application of computational fluid dynamics to wave action on structures},
+	author={Higuera, P},
+	journal={PhD. Universidade de Cantabria},
+	year={2015}
+}
+@phdthesis{poncet2021,
+	title={Characterization of wave impact loading on structures at full scale: field experiment, statistical analysis and 3D advanced numerical modeling},
+	author={Poncet, Pierre-Antoine},
+	year={2021},
+	school={Université de Pau et des Pays de l'Adour},
+	chapter={4},
+}
+@article{torrence1998,
+  title={A practical guide to wavelet analysis},
+  author={Torrence, Christopher and Compo, Gilbert P},
+  journal={Bulletin of the American Meteorological society},
+  volume={79},
+  number={1},
+  pages={61--78},
+  year={1998},
+  publisher={American Meteorological Society}
+}
+@article{dysthe2008,
+  title={Oceanic rogue waves},
+  author={Dysthe, Kristian and Krogstad, Harald E and M{\"u}ller, Peter},
+  journal={Annu. Rev. Fluid Mech.},
+  volume={40},
+  pages={287--310},
+  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}
+}
+@book{violeau2012,
+  title={Fluid mechanics and the SPH method: theory and applications},
+  author={Violeau, Damien},
+  year={2012},
+  publisher={Oxford University Press}
+}
+@article{violeau2007,
+  title={Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview},
+  author={Violeau, Damien and Issa, Reza},
+  journal={International Journal for Numerical Methods in Fluids},
+  volume={53},
+  number={2},
+  pages={277--304},
+  year={2007},
+  publisher={Wiley Online Library}
+}

nature/main.tex

@@ -0,0 +1,369 @@
+\documentclass[a4paper, twocolumn]{article}
+\usepackage{polyglossia} \usepackage{authblk}
+\usepackage[sfdefault]{inter}
+\usepackage[math-style=french]{unicode-math}
+\setmathfont{Fira Math}
+\usepackage{graphicx}
+\usepackage[hmargin=2.1cm, vmargin=2.97cm]{geometry}
+\usepackage{hyperref}
+\usepackage{siunitx}
+\sisetup{
+	mode=text,
+	reset-text-family=false,
+	reset-text-series=false,
+	reset-text-shape=false,
+	propagate-math-font=true,
+}
+
+\setmainlanguage{english}
+
+\usepackage[
+	backend=biber,
+	style=iso-authoryear,
+	sorting=nyt,
+]{biblatex}
+\bibliography{library}
+
+\hypersetup{
+	pdftitle={Analysis of the displacement of a large concrete block under an extreme wave},
+	pdfauthor={Edgar P. Burkhart}
+}
+
+\title{Analysis of the displacement of a large concrete block under an extreme wave}
+\author[1]{Edgar P. Burkhart}
+\author[*,1]{Stéphane Abadie}
+
+\affil[1]{Université de Pau et des Pays de l’Adour, E2S-UPPA,  SIAME, France}
+\affil[*]{Corresponding Author, stephane.abadie@univ-pau.fr}
+
+\begin{document}
+\maketitle
+
+\section{Introduction}
+% Displacement of blocks studies
+Displacement of large blocks or boulders by waves is an interesting phenomenon in the study of extreme historical
+coastal events. The existence of block deposits at unusual heights can be a clue to past events such as extreme storms
+or tsunamis. For instance, \textcite{cox2018} studied coastal deposits on the coast of Ireland in relation to the storms
+from winter 2013--2014, and extracted criteria for analysing such deposits. Similarly, \textcite{shah2013} found boulder
+deposits on the mediterranean coast to be evidence of extreme storms in the Little Ice Age.
+
+% Need for analytical equations
+In order for those studies to be possible, analytical criterias are needed in order to ascertain the cause of the
+displacement of a block. \textcite{nott1997,nott2003} proposed a set of equations that have been widely used for that
+purpose. Those equations rely on an equilibrium relation between the lift force produced by a wave and restraining
+forces depending on the initial setting of the block, allowing to extract a minimal flow velocity necessary for movement
+initiation. A parametrisation of waves depending on their source is also used to provide minimal wave heights depending
+on the type of scenario --- wave or tsunami. Those equations were later revised by \textcite{nandasena2011}, as they
+were found to be partially incorrect. A revised formulation based on the same considerations was provided.
+
+The assumptions on which \textcite{nott2003, nandasena2011} are based were then critisized by \textcite{weiss2015}. In
+fact, according to them, the initiation of movement is not sufficient to guarantee block displacement.
+\textcite{weiss2015} highlights the importance of the time dependency on block displacement. A method is proposed that
+allows to find the wave amplitude that lead to block displacement. Additionally, more recent research by
+\textcite{lodhi2020} has shown that the equations proposed by \textcite{nott2003, nandasena2011} tend to overestimate
+the minimum flow velocity needed to displace a block.
+
+% Lack of observations -> observation
+Whether it is \textcite{nott2003}, \textcite{nandasena2011} or \textcite{weiss2015}, all the proposed analytical
+equations suffer from a major flaw: they are all based on very simplified analytical models and statistical analysis.
+Unfortunately, no block displacement event seems to have been observed directly in the past, and those events are
+difficult to predict.
+
+In this paper, we study such an event. On February 28, 2017, a \SI{50}{\tonne} concrete block was dropped by a wave on
+the crest of the Artha breakwater (Figure~\ref{fig:photo}). Luckily, the event was captured by a photographer, and a
+wave buoy located \SI{1.2}{\km} offshore captured the seastate. Information from the photographer allowed to establish
+the approximate time at which the block displacement occured. The goal of this paper is to model the hydrodynamic
+conditions near the breakwater that lead to the displacement of the \SI{50}{\tonne} concrete block.
+
+% Modeling flow accounting for porous media
+Several approaches can be used when modelling flow near a breakwater. Depth-averaged models can be used to study the
+transformation of waves on complex bottoms. Studying the hydrodynamic conditions under the surface can be achieved
+using smoothed-particles hydrodynamics (SPH) or volume of fluid (VOF) models. SPH models rely on a Lagrangian
+representation of the fluid \parencite{violeau2012}, while VOF models rely on an Eulerian representation. VOF models
+are generally more mature for the study of multiphase incompressible flows, while SPH models generally require more
+processing power for similar results \parencite{violeau2007}.
+
+In this paper, we first use a one-dimensionnal depth-averaged non-linear non-hydrostatic model to verify that the
+signal measured by the wave buoy can be used as an incident wave input for the determination of hydrodynamic conditions
+near the breakwater. For this model, we use a SWASH model \parencite{zijlema2011} already calibrated by
+\textcite{poncet2021} on a domain reaching \SI{1450}{\m} offshore of the breakwater.
+
+Then, we use a nested VOF model in two vertical dimensions that uses the output from the larger scale SWASH model as
+initial and boundary conditions to obtain the hydrodynamic conditions on the breakwater. The model uses olaFlow
+\parencite{higuera2015}, a VOF model based on volume averaged Reynolds averaged Navier-Stokes (VARANS) equations, and
+which relies on a macroscopic representation of the porous armour of the breakwater. The model is qualitatively
+calibrated using photographs from the storm of February 28, 2017. Results from the nested models are finally compared
+to the analytical equations provided by \textcite{nandasena2011}.
+
+\begin{figure*}
+	\centering
+	\includegraphics[height=.4\textwidth]{fig/pic1.jpg}
+	\includegraphics[height=.4\textwidth]{fig/pic2.jpg}
+	\caption{Photographs taken during and after the wave that displaced a \SI{50}{\tonne} concrete block onto the Artha
+	breakwater.}\label{fig:photo}
+\end{figure*}
+
+\section{Results}
+\subsection{Identified wave}
+
+Preliminary work with the photographer allowed to identify the time at which the block displacement event happened.
+Using the data from the wave buoy located \SI{1250}{\m} offshore of the Artha breakwater, a seamingly abnormally large
+wave of \SI{14}{\m} amplitude was identified that is supposed to have led to the block displacement.
+
+Initial analysis of the buoy data plotted in Figure~\ref{fig:wave} shows that the movement of the buoy follows two
+orbitals that correspond to an incident wave direction. These results would indicate that the identified wave is
+essentially an incident wave, with a minor reflected component.
+
+The wavelet power spectrum displayed in Figure~\ref{fig:wavelet} highlights a primary infragravity wave in the signal,
+with a period of over \SI{30}{\s}.
+
+\begin{figure*}
+	\centering
+	\includegraphics{fig/ts.pdf}
+	\includegraphics{fig/out_orbitals.pdf}
+	\caption{\textit{Left}: Free surface measured during the extreme wave measured on February 28, 2017 at 17:23UTC.
+	\textit{Right}: Trajectory of the wave buoy during the passage of this particular wave.}\label{fig:wave}
+\end{figure*}
+
+\subsection{Reflection analysis}
+
+The results from the large scale SWASH model using two configurations --- one of them being the real bathymetry, and
+the other being a simplified bathymetry without the breakwater --- are compared in Figure~\ref{fig:swash}. The results
+obtained with both simulations show a maximum wave amplitude of \SI{13.9}{\m} for the real bathymetry, and
+\SI{12.1}{\m} in the case where the breakwater is removed.
+
+\begin{figure*}
+	\centering
+	\includegraphics{fig/maxw.pdf}
+	\caption{Free surface elevation obtained with the SWASH model in two configurations. \textit{Case 1}: With breakwater;
+	\textit{Case 2}: Without breakwater.}\label{fig:swash}
+\end{figure*}
+
+\subsection{Wave transformation}
+
+The free surface obtained with the SWASH model using raw buoy measurements as an elevation boundary condition is plotted
+in Figure~\ref{fig:swash_trans}. Those results display a strong transformation of the wave between the buoy and the
+breakwater. Not only the amplitude, but also the shape of the wave are strongly impacted by the propagation over the
+domain. While the amplitude of the wave is reduced as the wave propagates shorewards, the length of the trough and the
+crest increases, with a zone reaching \SI{400}{\m} long in front of the wave where the water level is below \SI{0}{\m}.
+
+\begin{figure*}
+	\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 front.}\label{fig:swash_trans}
+\end{figure*}
+
+In an attempt to understand the identified wave, a wavelet analysis is conducted on raw buoy data as well as at
+different points along the SWASH model using the method proposed by \textcite{torrence1998}. The results are displayed
+in Figure~\ref{fig:wavelet} and Figure~\ref{fig:wavelet_sw}. The wavelet power spectrum shows that the major component
+in identified rogue waves is a high energy infragravity wave, with a period of around \SI{60}{\s}. 
+
+The SWASH model seems to indicate that the observed transformation of the wave can be characterized by a transfer of
+energy from the infragravity band to shorter waves from around \SI{600}{\m} to \SI{300}{\m}, and returning to the
+infragravity band at \SI{200}{\m}.
+
+\begin{figure*}
+	\centering
+	\includegraphics{fig/wavelet.pdf}
+	\caption{Normalized wavelet power spectrum from the raw buoy timeseries for identified rogue waves on february 28,
+	2017.}\label{fig:wavelet}
+\end{figure*}
+\begin{figure*}
+	\centering
+	\includegraphics{fig/wavelet_sw.pdf}
+	\caption{Normalized wavelet power spectrum along the SWASH domain.}\label{fig:wavelet_sw}
+\end{figure*}
+
+\subsection{Hydrodynamic conditions on the breakwater}
+
+The two-dimensionnal olaFlow model near the breakwater allowed to compute the flow velocity near and on the breakwater
+during the passage of the identified wave. The results displayed in Figure~\ref{fig:U} show that the flow velocity
+reaches a maximum of \SI{14.5}{\m\per\s} towards the breakwater during the identified extreme wave. Although the
+maximum reached velocity is similar to earlier shorter waves, the flow velocity remains high for twice as long as
+during those earlier waves. The tail of the identified wave also exhibits a water level over \SI{5}{\m} for over
+\SI{40}{\s}.
+
+\begin{figure*}
+	\centering
+	\includegraphics{fig/U.pdf}
+	\caption{Horizontal flow velocity computed with the olaFlow model at $x=\SI{-20}{\m}$ on the breakwater armor.
+	Bottom: horizontal flow velocity at $z=\SI{5}{\m}$. The identified wave reaches this point around
+	$t=\SI{175}{\s}$.}\label{fig:U}
+\end{figure*}
+
+\section{Discussion}
+
+\subsection{Incident wave}
+
+According to the criteria proposed by \textcite{dysthe2008}, rogue waves can be defined as waves with an amplitude over
+twice the significant wave height over a given period. The identified wave fits this definition, as its amplitude is
+\SI{14.7}{\m}, over twice the significant wave height of \SI{6.3}{\m} on that day. According to \textcite{dysthe2008},
+rogue waves often occur from non-linear superposition of smaller waves. This seems to be what we observe on
+Figure~\ref{fig:wave}.
+
+As displayed in Figure~\ref{fig:wavelet}, a total of 4 rogue waves were identified on february 28, 2017 in the raw buoy
+timeseries using the wave height criteria proposed by \textcite{dysthe2008}. The wavelet power spectrum shows that a
+very prominent infragravity component is present, which usually corresponds to non-linear interactions of smaller
+waves. \textcite{dysthe2008} mentions that such waves in coastal waters are often the result of refractive focusing. On
+February 28, 2017, the frequency of rogue waves was found to be of 1 wave per 1627, which is considerably more than the
+excedance probability of 1 over 10\textsuperscript4 calculated by \textcite{dysthe2008}. Additionnal studies should be
+conducted to understand focusing and the formation of rogue waves in front of the Saint-Jean-de-Luz bay.
+
+An important point to note is that rogue waves are often short-lived: their nature means that they often separate into
+shorter waves shortly after appearing. A reason for which such rogue waves can be maintained over longer distances can
+be a change from a dispersive environment such as deep water to a non-dispersive environment. The bathymetry near the
+wave buoy (Figure~\ref{fig:bathy}) shows that this might be what we observe here, as the buoy is located near a step in
+the bathymetry, from around \SI{40}{\m} to \SI{20}{\m} depth.
+
+\subsection{Reflection analysis}
+
+The 13\% difference between those values highlights the existence of a notable amount of reflection at the buoy.
+Nonetheless, the gap between the values is still fairly small and the extreme wave identified on February 28, 2017 at
+17:23:08 could still be considered as an incident wave.
+
+Unfortunately, the spectrum wave generation method used by SWASH could not reproduce simlar waves to the one observed
+at the buoy. As mentionned by \textcite{dysthe2008}, such rogue waves cannot be deterministicly from the wave spectrum.
+For this reason, this study only allows us to observe the influence of reflection on short waves, while mostly ignoring
+infragravity waves. Those results are only useful if we consider that infragravity waves behave similarly to shorter
+waves regarding reflection.
+
+\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 $T+\SI{60}{\s}$ for instance, the water level is under \SI{0}{\m} for \SI{400}{\m}, and
+then over \SI{0}{\m} 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 $t=\SI{1500}{\s}$) 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 \SI{19.4}{\m\per\s} The results from the Olaflow model yield a maximal wave velocity during
+the displacement of the \SI{50}{\tonne} concrete block of \SI{14.5}{\m\per\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, similar flow velocities are 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.
+
+Although those results are a major step in a better understanding of block displacement in coastal regions, further
+work is needed to understand in more depth the formation and propagation of infragravity waves in the near-shore
+region. Furthermore, this study was limited to a single block displacement event, and further work should be done to
+obtain more measurements and observations of such events, although their rarity and unpredictability makes this task
+difficult.
+
+\section{Methods}
+
+\subsection{Buoy data analysis}
+
+\subsubsection{Rogue wave identification}
+
+Identifying rogue waves requires two main steps: computing the significant wave height, and computing the height of
+individual waves. The first step is straightforward: $H_s=4\sigma$, where $\sigma$ is the standard deviation of the
+surface elevation. Computing the height of individual waves is conducted using the zero-crossing method: the time domain
+is split in sections where water level is strictly positive or negative, and wave size is computed according to the
+maxima and minima in each zone. This method can fail to identify some waves or wrongly identify waves in case of
+measurement errors or in the case where a small oscillation around 0 occurs in the middle of a larger wave. In order to
+account for those issues, the signal is first fed through a low-pass filter to prevent high frequency oscillations of
+over \SI{0.2}{\Hz}.
+
+\subsubsection{Wavelet analysis}
+
+All wavelet analysis in this study is conducted using a continuous wavelet transform over a Morlet window. The wavelet
+power spectrum is normalized by the variance of the timeseries, following the method proposed by
+\textcite{torrence1998}. This analysis extracts a time-dependent power spectrum and allows to identify the composition
+of waves in a time-series.
+
+\subsection{SWASH models}
+
+\subsubsection{Domain}
+
+\begin{figure}
+	\centering
+	\includegraphics{fig/bathy2d.pdf}
+	\caption{Bathymetry in front of the Artha breakwater. The extremities of the line are the buoy and the
+	breakwater.}\label{fig:bathy}
+\end{figure}
+
+A \SI{1750}{\m} 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 \SI{1}{\m} was used for most of the domain
+(Figure~\ref{fig:bathy}).
+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 \SI{4}{\hour} in order to generate a fair range of conditions. The wave
+transformation study was conducted over a \SI{1}{\hour} 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.
+
+\subsection{Olaflow model}
+
+\begin{figure*}
+	\centering
+	\includegraphics{fig/aw_t0.pdf}
+	\caption{Domain studied with Olaflow. Initial configuration.}\label{fig:of}
+\end{figure*}
+
+\subsubsection{Domain}
+
+A \SI{150}{\m} long domain is built in order to obtain the hydrodynamic conditions on the Artha breakwater during the
+passage of the identified extreme wave. The bathymetry with \SI{50}{\cm} resolution from \textcite{poncet2021} is used.
+The domain extends \SI{30}{\m} up in order to be able to capture the largest waves hitting the breakwater. Measurements
+are extracted \SI{20}{\m} shorewards from the breakwater crest. The domain is displayed in Figure~\ref{fig:of}.
+
+A mesh in two-vertical dimensions with \SI{20}{\cm} resolution was generated using the interpolated bathymetry. As with
+the SWASH model, the porous armour was considered at a macroscopic scale.
+
+\subsubsection{Model}
+
+A volume-of-fluid (VOF) model in two-vertical dimensions based on volume-averaged Reynolds-averaged Navier-Stokes
+(VARANS) equations is used (olaFlow, \cite{higuera2015}). The model was initially setup using generic values for porous
+breakwater studies. A sensibility study conducted on the porosity parameters found the influence of these values on
+the final results to be very minor.
+
+The k-ω SST turbulence model was used, as it produced much more realistic results than the default k-ε model,
+especially compared to the photographs from the storm of February 28, 2017. The k-ε model yielded very high viscosity
+and thus strong dissipation in the entire domain, preventing an accurate wave breaking representation.
+
+\subsubsection{Boundary conditions}
+
+Initial and boundary conditions were generated using the output from the SWASH wave transformation model. The boundary
+condition is generated by a paddle-like wavemaker, using the water level and depth-averaged velocity computed by the
+SWASH model.
+
+\printbibliography
+\end{document}

tasks.md

@@ -18,3 +18,18 @@ Olaflow comparison with photos
 Comparison of olaflow output with block displacement theories
 
 Format rapport: Journal of Geophysical Research
+
+
+
+Ajouter Figures: photos: vague & bloc sur la digue, wavelet analysis bouée autres vagues,
+Snapshot vagues sortie olaflow
+
+Étoffer un peu contenu
+
+Figure 6: Line plot en 1 point de la vitesse du courant
+
+Faire lien entre photos et splashs dans swash
+
+Génération vague scélérate : combinaison + dispersion -> zone non dispersive : ajouter profil bathymétrie
+
+Tester bathy plane avec swash pour voir si transfert énergie IG -> G