Discussion, methods swash

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}
+}

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}