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[latex]
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engine=xelatex
|
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main=main.tex
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out=nature.pdf
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137
nature/library.bib
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nature/library.bib
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@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}
|
||||
}
|
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nature/main.tex
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nature/main.tex
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\documentclass[a4paper, twocolumn]{article}
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\usepackage{polyglossia} \usepackage{authblk}
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\usepackage[sfdefault]{inter}
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\usepackage[math-style=french]{unicode-math}
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\setmathfont{Fira Math}
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\usepackage{graphicx}
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\usepackage[hmargin=2.1cm, vmargin=2.97cm]{geometry}
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\usepackage{hyperref}
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\usepackage{siunitx}
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\sisetup{
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mode=text,
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reset-text-family=false,
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reset-text-series=false,
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reset-text-shape=false,
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propagate-math-font=true,
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}
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\setmainlanguage{english}
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\usepackage[
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backend=biber,
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style=iso-authoryear,
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sorting=nyt,
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]{biblatex}
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\bibliography{library}
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\hypersetup{
|
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pdftitle={Analysis of the displacement of a large concrete block under an extreme wave},
|
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pdfauthor={Edgar P. Burkhart}
|
||||
}
|
||||
|
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\title{Analysis of the displacement of a large concrete block under an extreme wave}
|
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\author[1]{Edgar P. Burkhart}
|
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\author[*,1]{Stéphane Abadie}
|
||||
|
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\affil[1]{Université de Pau et des Pays de l’Adour, E2S-UPPA, SIAME, France}
|
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\affil[*]{Corresponding Author, stephane.abadie@univ-pau.fr}
|
||||
|
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\begin{document}
|
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\maketitle
|
||||
|
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\section{Introduction}
|
||||
% Displacement of blocks studies
|
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Displacement of large blocks or boulders by waves is an interesting phenomenon in the study of extreme historical
|
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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
|
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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.
|
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Unfortunately, no block displacement event seems to have been observed directly in the past, and those events are
|
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difficult to predict.
|
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|
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In this paper, we study such an event. On February 28, 2017, a \SI{50}{\tonne} concrete block was dropped by a wave on
|
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the crest of the Artha breakwater (Figure~\ref{fig:photo}). Luckily, the event was captured by a photographer, and a
|
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wave buoy located \SI{1.2}{\km} offshore captured the seastate. Information from the photographer allowed to establish
|
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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.
|
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|
||||
% Modeling flow accounting for porous media
|
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Several approaches can be used when modelling flow near a breakwater. Depth-averaged models can be used to study the
|
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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
|
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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.
|
||||
|
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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}.
|
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|
||||
\begin{figure*}
|
||||
\centering
|
||||
\includegraphics[height=.4\textwidth]{fig/pic1.jpg}
|
||||
\includegraphics[height=.4\textwidth]{fig/pic2.jpg}
|
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\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
|
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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}
|
15
tasks.md
15
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
|
||||
|
|
Loading…
Reference in a new issue