Results from swash 1

nature/main.tex

@@ -1,6 +1,7 @@
 \documentclass[a4paper, twocolumn]{article}
 \usepackage{polyglossia} \usepackage{authblk}
 \usepackage[sfdefault]{inter}
+\usepackage{graphicx}
 
 \setmainlanguage{english}
 
@@ -48,9 +49,9 @@ 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 +62,54 @@ 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{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}