From f7d287394fd1af80725bedb80e6911aff50f0c59 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 6 Jun 2022 09:41:23 +0200 Subject: [PATCH 01/20] Nature: start introduction --- nature/kalliope.conf | 4 +++ nature/library.bib | 86 ++++++++++++++++++++++++++++++++++++++++++++ nature/main.tex | 66 ++++++++++++++++++++++++++++++++++ 3 files changed, 156 insertions(+) create mode 100644 nature/kalliope.conf create mode 100644 nature/library.bib create mode 100644 nature/main.tex diff --git a/nature/kalliope.conf b/nature/kalliope.conf new file mode 100644 index 0000000..0e55077 --- /dev/null +++ b/nature/kalliope.conf @@ -0,0 +1,4 @@ +[latex] +engine=xelatex +main=main.tex +out=nature.pdf diff --git a/nature/library.bib b/nature/library.bib new file mode 100644 index 0000000..bd2cafa --- /dev/null +++ b/nature/library.bib @@ -0,0 +1,86 @@ +@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} +} diff --git a/nature/main.tex b/nature/main.tex new file mode 100644 index 0000000..518ac7f --- /dev/null +++ b/nature/main.tex @@ -0,0 +1,66 @@ +\documentclass[a4paper, twocolumn]{article} +\usepackage{polyglossia} +\usepackage{authblk} + +\setmainlanguage{english} + +\usepackage[ + backend=biber, + style=iso-authoryear, + sorting=nyt, +]{biblatex} +\bibliography{library} + +\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 \citeauthor{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. + +% 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 simplified analytical models and statistical analysis. +Unfortunately, no block displacement event seems to have been observed directly in the past. + +In this paper, we study such an event. In february 2017, a 50T concrete block was dropped by a wave on the crest of the +Artha breakwater. Luckily, the event was captured by a photographer, and a wave buoy located 1.2km 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 50T concrete block. + +% Modeling flow accounting for porous media +Several approaches can be used when modelling flow near a breakwater. + +\section{Results} + +\section{Discussion} + +\section{Methods} +\printbibliography +\end{document} From 384481c4e4b8eeda42575af603c2fdaf33586373 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 6 Jun 2022 09:53:23 +0200 Subject: [PATCH 02/20] Use inter sf font --- nature/main.tex | 1 + 1 file changed, 1 insertion(+) diff --git a/nature/main.tex b/nature/main.tex index 518ac7f..cd010cc 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -1,6 +1,7 @@ \documentclass[a4paper, twocolumn]{article} \usepackage{polyglossia} \usepackage{authblk} +\usepackage[sfdefault]{inter} \setmainlanguage{english} From 174b764b3a56f827cf70e37516e3908daf40c7c3 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 6 Jun 2022 09:56:14 +0200 Subject: [PATCH 03/20] Testing kalliope --- nature/main.tex | 2 ++ 1 file changed, 2 insertions(+) diff --git a/nature/main.tex b/nature/main.tex index cd010cc..2d3274a 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -58,6 +58,8 @@ the displacement of the 50T concrete block. % Modeling flow accounting for porous media Several approaches can be used when modelling flow near a breakwater. +Testing kalliope + \section{Results} \section{Discussion} From 564127e5b322210baf788aa51991e23d3d3517d1 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 7 Jun 2022 09:23:19 +0200 Subject: [PATCH 04/20] Introduction --- nature/library.bib | 12 ++++++++++++ nature/main.tex | 20 +++++++++++++++----- 2 files changed, 27 insertions(+), 5 deletions(-) diff --git a/nature/library.bib b/nature/library.bib index bd2cafa..ee1285c 100644 --- a/nature/library.bib +++ b/nature/library.bib @@ -84,3 +84,15 @@ journal={PhD. Universidade de Cantabria}, year={2015} } +@article{poncet2022, + title = {In-situ measurements of energetic depth-limited wave loading}, + journal = {Applied Ocean Research}, + volume = {125}, + pages = {103216}, + year = {2022}, + issn = {0141-1187}, + doi = {https://doi.org/10.1016/j.apor.2022.103216}, + url = {https://www.sciencedirect.com/science/article/pii/S0141118722001572}, + author = {P.A. Poncet and B. Liquet and B. Larroque and D. D’Amico and D. Sous and S. Abadie}, + keywords = {Wave impact, Breaking wave, Loading, Breakwater, Field measurement, Pressure impulse, Multiple linear regression, Wind, Water level}, +} diff --git a/nature/main.tex b/nature/main.tex index 2d3274a..1a64585 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -1,6 +1,5 @@ \documentclass[a4paper, twocolumn]{article} -\usepackage{polyglossia} -\usepackage{authblk} +\usepackage{polyglossia} \usepackage{authblk} \usepackage[sfdefault]{inter} \setmainlanguage{english} @@ -49,16 +48,27 @@ Whether it is \textcite{nott2003}, \textcite{nandasena2011} or \textcite{weiss20 equations suffer from a major flaw; they are all based on simplified analytical models and statistical analysis. Unfortunately, no block displacement event seems to have been observed directly in the past. -In this paper, we study such an event. In february 2017, a 50T concrete block was dropped by a wave on the crest of the +In this paper, we study such an event. On February 28, 2017, a 50T concrete block was dropped by a wave on the crest of the Artha breakwater. Luckily, the event was captured by a photographer, and a wave buoy located 1.2km 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 50T concrete block. % Modeling flow accounting for porous media -Several approaches can be used when modelling flow near a breakwater. +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, while VOF models rely on an Eulerian representation. VOF models are generally more mature +for the study of multiphase incompressible flows. -Testing kalliope +In this paper, we use two nested models: a large scale one-dimensionnal model to study the transformation of the wave +from the wave buoy to the proximity of the breakwater, and a VOF model in two vertical dimensions to study the +hydrodynamic conditions near the breakwater. The large scale model uses a depth-averaged non-linear non-hydrostatic +model that was already calibrated by \textcite{poncet2022}. The nested model is a VOF model based on volume averaged +Reynolds averaged Navier-Stokes (VARANS) equations and 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 compared to the analytical equations provided by \textcite{nandasena2011}. \section{Results} From d1b6819e0c267f4b7d9a22c81a436e2ad953457a Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 7 Jun 2022 09:25:55 +0200 Subject: [PATCH 05/20] Add model names in introduction --- nature/main.tex | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/nature/main.tex b/nature/main.tex index 1a64585..f0e4a65 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -63,10 +63,11 @@ for the study of multiphase incompressible flows. In this paper, we use two nested models: a large scale one-dimensionnal model to study the transformation of the wave from the wave buoy to the proximity of the breakwater, and a VOF model in two vertical dimensions to study the -hydrodynamic conditions near the breakwater. The large scale model uses a depth-averaged non-linear non-hydrostatic -model that was already calibrated by \textcite{poncet2022}. The nested model is a VOF model based on volume averaged -Reynolds averaged Navier-Stokes (VARANS) equations and a macroscopic representation of the porous armour of the -breakwater. The model is qualitatively calibrated using photographs from the storm of February 28, 2017. +hydrodynamic conditions near the breakwater. The large scale model uses SWASH \parencite{zijlema2011} a depth-averaged +non-linear non-hydrostatic model that was already calibrated by \textcite{poncet2022}. The nested model uses olaFlow +\parencite{higuera2015}, a VOF model based on volume averaged Reynolds averaged Navier-Stokes (VARANS) equations 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 compared to the analytical equations provided by \textcite{nandasena2011}. From ec051a20545223bb53080e385fa804846f7c47c6 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 7 Jun 2022 11:04:23 +0200 Subject: [PATCH 06/20] Finalise introduction --- nature/main.tex | 26 +++++++++++++++----------- 1 file changed, 15 insertions(+), 11 deletions(-) diff --git a/nature/main.tex b/nature/main.tex index f0e4a65..426b0ab 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -48,9 +48,9 @@ Whether it is \textcite{nott2003}, \textcite{nandasena2011} or \textcite{weiss20 equations suffer from a major flaw; they are all based on simplified analytical models and statistical analysis. Unfortunately, no block displacement event seems to have been observed directly in the past. -In this paper, we study such an event. On February 28, 2017, a 50T concrete block was dropped by a wave on the crest of the -Artha breakwater. Luckily, the event was captured by a photographer, and a wave buoy located 1.2km offshore captured -the seastate. Information from the photographer allowed to establish the approximate time at which the block +In this paper, we study such an event. On February 28, 2017, a 50T concrete block was dropped by a wave on the crest of +the Artha breakwater. Luckily, the event was captured by a photographer, and a wave buoy located 1.2km 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 50T concrete block. @@ -61,17 +61,21 @@ using smoothed-particles hydrodynamics (SPH) or volume of fluid (VOF) models. SP representation of the fluid, while VOF models rely on an Eulerian representation. VOF models are generally more mature for the study of multiphase incompressible flows. -In this paper, we use two nested models: a large scale one-dimensionnal model to study the transformation of the wave -from the wave buoy to the proximity of the breakwater, and a VOF model in two vertical dimensions to study the -hydrodynamic conditions near the breakwater. The large scale model uses SWASH \parencite{zijlema2011} a depth-averaged -non-linear non-hydrostatic model that was already calibrated by \textcite{poncet2022}. The nested model uses olaFlow -\parencite{higuera2015}, a VOF model based on volume averaged Reynolds averaged Navier-Stokes (VARANS) equations 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. +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{poncet2022} on a domain reaching 1450m offshore of the breakwater. -Results from the nested models are compared to the analytical equations provided by \textcite{nandasena2011}. +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 models 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}. \section{Results} +\subsection{Reflection analysis} + \section{Discussion} From 95785f9df532367ece2830e8b7c27c18f21bd087 Mon Sep 17 00:00:00 2001 From: "Edgar P. 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Results from t to the analytical equations provided by \textcite{nandasena2011}. \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 1250m offshore of the Artha breakwater, a seamingly abnormally large wave of +14m amplitude was identified that is supposed to have lead 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. + +\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 13.9m for the real bathymetry, and 12.1m in the case +where the breakwater is removed. + +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. + +\begin{figure*} + \centering + \includegraphics{fig/maxw.pdf} + \caption{Free surface obtained with the SWASH model in two configurations. \textit{Case 1}: With breakwater; + \textit{Case 2}: Without breakwater.}\label{fig:swash} +\end{figure*} \section{Discussion} From f113808de4ffbe1e484a7b4eb4a0e4dcb4c81aff Mon Sep 17 00:00:00 2001 From: "Edgar P. 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b/nature/library.bib index d44e247..ea2c717 100644 --- a/nature/library.bib +++ b/nature/library.bib @@ -91,3 +91,13 @@ 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} +} diff --git a/nature/main.tex b/nature/main.tex index 19284d3..f31441d 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -126,6 +126,28 @@ the crest increases, with a zone reaching 400m long in front of the wave where t qualitatively estimated position of the wave crest.}\label{fig:swash_trans} \end{figure*} +\subsection{Wavelet analysis} + +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 the identified wave is a high energy infragravity wave, with a period of around 60s. + +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 600m to 300m, and returning to the infragravity band at +200m. + +\begin{figure*} + \centering + \includegraphics{fig/wavelet9312.pdf} + \caption{Normalized wavelet power spectrum from the raw buoy timeseries.}\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 @@ -145,6 +167,8 @@ exhibits a water level over 5m for over 40s. \section{Discussion} + + \section{Methods} \printbibliography \end{document} From 9fec212d98d648ef8f1c11af24023f5551bbf595 Mon Sep 17 00:00:00 2001 From: "Edgar P. 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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 From 9ece349d435531e7fd8585eee0bac0f6282c0ed0 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 4 Jul 2022 19:20:46 +0200 Subject: [PATCH 20/20] End report --- nature/fig/U.pdf | Bin 111608 -> 112135 bytes nature/fig/bathy2d.pdf | Bin 0 -> 11362 bytes nature/fig/pic1.jpg | Bin 0 -> 1864363 bytes nature/fig/pic2.jpg | Bin 0 -> 2564565 bytes nature/fig/wavelet.pdf | Bin 0 -> 62695 bytes nature/fig/wavelet9312.pdf | Bin 38860 -> 0 bytes nature/fig/wavelet_sw.pdf | Bin 110706 -> 113761 bytes nature/library.bib | 16 ++++ nature/main.tex | 152 ++++++++++++++++++++++--------------- 9 files changed, 107 insertions(+), 61 deletions(-) create mode 100644 nature/fig/bathy2d.pdf create mode 100755 nature/fig/pic1.jpg create mode 100755 nature/fig/pic2.jpg create mode 100644 nature/fig/wavelet.pdf delete mode 100644 nature/fig/wavelet9312.pdf diff --git a/nature/fig/U.pdf b/nature/fig/U.pdf index 33ba638b3e1c7e227ff089da4140205cee4904e2..f7ce199b5b7751bf13feec110e1c48596cc075e7 100644 GIT binary patch delta 105374 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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} +} diff --git a/nature/main.tex b/nature/main.tex index 3e2470d..7114d49 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -56,47 +56,59 @@ initiation. A parametrisation of waves depending on their source is also used to 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 \citeauthor{nott2003, nandasena2011} are based were then critisized by \textcite{weiss2015}. In +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. +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 simplified analytical models and statistical analysis. -Unfortunately, no block displacement event seems to have been observed directly in the past. +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. 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. +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, while VOF models rely on an Eulerian representation. VOF models are generally more mature for the study of -multiphase incompressible flows. +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. +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 models uses olaFlow +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}. +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 lead to the block displacement. +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 @@ -115,14 +127,10 @@ with a period of over \SI{30}{\s}. \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. - -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. +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 @@ -146,12 +154,10 @@ crest increases, with a zone reaching \SI{400}{\m} long in front of the wave whe qualitatively estimated position of the wave front.}\label{fig:swash_trans} \end{figure*} -\subsection{Wavelet analysis} - 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 the identified wave is a high energy infragravity wave, with a period of around \SI{60}{\s}. +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 @@ -159,8 +165,9 @@ infragravity band at \SI{200}{\m}. \begin{figure*} \centering - \includegraphics{fig/wavelet9312.pdf} - \caption{Normalized wavelet power spectrum from the raw buoy timeseries.}\label{fig:wavelet} + \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 @@ -172,16 +179,17 @@ infragravity band at \SI{200}{\m}. 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 slightly lower than earlier shorter waves (at $t=\SI{100}{\s}$ and $t=\SI{120}{\s}$, with a maximum -velocity of \SI{17.3}{\m\per\s}), 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}. +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. The - identified wave reaches this point around $t=\SI{175}{\s}$.}\label{fig:U} + \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} @@ -194,12 +202,19 @@ twice the significant wave height over a given period. The identified wave fits rogue waves often occur from non-linear superposition of smaller waves. This seems to be what we observe on Figure~\ref{fig:wave}. -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. +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} @@ -207,10 +222,11 @@ The 13\% difference between those values highlights the existence of a notable a 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. +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} @@ -236,11 +252,16 @@ Those results tend to confirm recent research by \textcite{lodhi2020}, where it 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. +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} @@ -261,14 +282,23 @@ over \SI{0.2}{\Hz}. 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}. +\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. +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. @@ -322,12 +352,12 @@ the SWASH model, the porous armour was considered at a macroscopic scale. 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 a minor influence of these values on -the final results. +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. +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}

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zdx9^=QaA*>3QJ1}w7-qu)+exnf!=?mN!Xc@fBC(|r5hnz*eu{%*eon8rXO0xn89vh zXl85z++l0DnsEi2frX)kx#{%#s~KNA8kw0I87LTlfI^-E7nosUU}^%~28SYMYGP<= zh9+iaZf0q|oqH{#I8&yPnTaLPUKBk*bBs*U#DL})o1lpS%`rz;2XvyTF`7CHLrY`R W>D}uYU3e^v3@nYfR8?L5-M9cuYFsb? diff --git a/nature/library.bib b/nature/library.bib index ea2c717..0c7b7de 100644 --- a/nature/library.bib +++ b/nature/library.bib @@ -101,3 +101,12 @@ 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} +} diff --git a/nature/main.tex b/nature/main.tex index f31441d..7c2d820 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -85,6 +85,9 @@ Initial analysis of the buoy data plotted in Figure~\ref{fig:wave} shows that th 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{wavelet} highlights a primary infragravity wave in the signal, with +a period of over 30s. + \begin{figure*} \centering \includegraphics{fig/ts.pdf} @@ -167,7 +170,18 @@ exhibits a water level over 5m for over 40s. \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. + +\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. + +\subsection{} \section{Methods} \printbibliography From db148e8bdd8f636fc0337c420977d95d82634c1f Mon Sep 17 00:00:00 2001 From: "Edgar P. 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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{wavelet} highlights a primary infragravity wave in the signal, with +The wavelet power spectrum displayed in Figure~\ref{fig:wavelet} highlights a primary infragravity wave in the signal, with a period of over 30s. \begin{figure*} @@ -173,7 +173,16 @@ exhibits a water level over 5m for over 40s. \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. +twice the significant wave height over a given period. The identified wave fits this definition, as its amplitude is +14.7m, over twice the significant wave height of 6.3m 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}. + +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. \subsection{Reflection analysis} @@ -181,7 +190,12 @@ The 13\% difference between those values highlights the existence of a notable a 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. -\subsection{} +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. + +\subsection{Wave transformation} \section{Methods} \printbibliography From acfb2ee382b5aa8a7a23b358ad7374e69ed4022e Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 28 Jun 2022 15:05:11 +0200 Subject: [PATCH 16/20] Discussion, methods swash --- nature/library.bib | 9 ++++++ nature/main.tex | 73 ++++++++++++++++++++++++++++++++++++++++++++-- 2 files changed, 80 insertions(+), 2 deletions(-) diff --git a/nature/library.bib b/nature/library.bib index 0c7b7de..40a67c8 100644 --- a/nature/library.bib +++ b/nature/library.bib @@ -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} +} diff --git a/nature/main.tex b/nature/main.tex index 43ebf06..c9ed757 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -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} From 2422c412f73772c72a572fb03f889d4d16fdcd4a Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 28 Jun 2022 16:08:48 +0200 Subject: [PATCH 17/20] Methods olaflow --- nature/main.tex | 37 ++++++++++++++++++++++++++++++++++++- 1 file changed, 36 insertions(+), 1 deletion(-) diff --git a/nature/main.tex b/nature/main.tex index c9ed757..cfef9d6 100644 --- a/nature/main.tex +++ b/nature/main.tex @@ -1,8 +1,9 @@ -\documentclass[a4paper, twocolumn]{article} +\documentclass[a4paper, twocolumn, draft]{article} \usepackage{polyglossia} \usepackage{authblk} \usepackage[sfdefault]{inter} \usepackage{graphicx} \usepackage[hmargin=2.1cm, vmargin=2.97cm]{geometry} +\usepackage{hyperref} \setmainlanguage{english} @@ -13,6 +14,11 @@ ]{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} @@ -261,11 +267,40 @@ shorewards boundary to prevent wave reflection on the boundary. In the reflectio 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} + +\subsubsection{Domain} + +A 150m 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 50cm resolution from \textcite{poncet2021} is used. The domain +extends 30m up in order to be able to capture the largest waves hitting the breakwater. Measurements are extracted 20m +shorewards from the breakwater crest. The domain is displayed in Figure~\ref{fig:of}. + +A mesh in two-vertical dimensions with 20cm resolution was generated using the interpolated bathymetry. As with the +SWASH model, the porous armour was considered at a macroscopic scale. + \begin{figure*} \centering \includegraphics{fig/aw_t0.pdf} \caption{Domain studied with Olaflow. Initial configuration.}\label{fig:of} \end{figure*} +\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 a minor influence of these +values on the final results. + +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} From c90e3b8b86836a40a82813de6f814d98688027d5 Mon Sep 17 00:00:00 2001 From: "Edgar P. 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