Discussion, methods swash
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@ -110,3 +110,12 @@
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year={2008},
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publisher={Annual Reviews}
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}
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@article{lodhi2020,
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title={The role of hydrodynamic impact force in subaerial boulder transport by tsunami—Experimental evidence and revision of boulder transport equation},
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author={Lodhi, Hira A and Hasan, Haider and Nandasena, NAK},
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journal={Sedimentary Geology},
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volume={408},
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pages={105745},
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year={2020},
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publisher={Elsevier}
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}
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@ -2,6 +2,7 @@
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\usepackage{polyglossia} \usepackage{authblk}
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\usepackage[sfdefault]{inter}
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\usepackage{graphicx}
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\usepackage[hmargin=2.1cm, vmargin=2.97cm]{geometry}
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\setmainlanguage{english}
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@ -126,7 +127,7 @@ the crest increases, with a zone reaching 400m long in front of the wave where t
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\centering
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\includegraphics{fig/x.pdf}
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\caption{Propagation of the wave supposed to be responsible for the block displacement; highlighted zone:
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qualitatively estimated position of the wave crest.}\label{fig:swash_trans}
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qualitatively estimated position of the wave front.}\label{fig:swash_trans}
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\end{figure*}
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\subsection{Wavelet analysis}
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@ -162,7 +163,6 @@ exhibits a water level over 5m for over 40s.
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\begin{figure*}
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\centering
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\includegraphics{fig/aw_t0.pdf}
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\includegraphics{fig/U.pdf}
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\caption{Horizontal flow velocity computed with the olaFlow model at x=-20m on the breakwater armor. The identified
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wave reaches this point around t=175s.}\label{fig:U}
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@ -197,6 +197,75 @@ infragravity waves.
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\subsection{Wave transformation}
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The SWASH model yields a strongly changing wave over the domain, highlighting the highly complex composition of this
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wave. Although the peak of the amplitude of the wave is reduced as the wave propagates, the length of the wave is
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highlighted by the results. At T+60s for instance, the water level is under 0m for 400m, and then over 0m for around
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the same length, showing the main infragavity component of the studied wave.
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The wavelet analysis conducted at several points along the domain (Figure~\ref{fig:wavelet_sw}) show that the energy of
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the studied wave (slightly before t=1500s) initially displays a strong infragravity component. Energy is then
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transfered from the infragravity band towards shorter waves, and back to the infragravity band. This behavior is quite
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unexpected, and further investigations should be conducted to understand and validate those results.
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\subsection{Hydrodynamic conditions on the breakwater}
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The hydrodynamic conditions on the breakwater are the main focus of this study. Considering an initially submerged
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block, analytical equations proposed by \textcite{nandasena2011} yield a minimal flow velocity that would lead to block
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displacement by saltation of 19.4m/s. The results from the Olaflow model yield a maximal wave velocity during the
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displacement of the 50T concrete block of 14.5m/s. The results from the model are 25\% lower than the analytical value.
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Those results tend to confirm recent research by \textcite{lodhi2020}, where it was found that the block displacement
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threshold tend to overestimate the minimal flow velocity needed for block movement, although further validation of the
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model that is used would be needed to confirm those findings.
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Additionally, the flow velocity that is reached during the identified wave is not the highest that is reached in the
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model. Other shorter waves yield similar flow velocities on the breakwater, but in a smaller timeframe. The importance
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of time dependency in studying block displacement would be in accordance with research from \textcite{weiss2015}, who
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suggested that the use of time-dependent equations for block displacement would lead to a better understanding of the
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phenomenon.
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\section{Methods}
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\subsection{SWASH models}
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\subsubsection{Domain}
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A 1750m long domain is constructed in order to study wave reflection and wave transformation over the bottom from the
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wave buoy to the breakwater. Bathymetry with a resolution of around 1m was used for most of the domain. The breakwater
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model used in the study is taken from \textcite{poncet2021}. A smoothed section is created and considered as a porous
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media in the model.
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A second domain is constructed for reflection analysis. The second model is the same as the first, excepted that the
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breakwater is replaced by a smooth slope in order to remove the reflection generated by the structure.
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The reflection analysis is conducted over 4h in order to generate a fair range of conditions. The wave transformation
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study was conducted over a 1h timeframe in order to allow the model to reach steady-state before the studied wave was
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generated.
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\subsubsection{Model}
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A non-linear non-hydrostatic shallow water model (SWASH, \cite{zijlema2011}) is used to model wave reflection and
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transformation on the studied domain. The study is conducted using a layered one-dimensional model, that allows to
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consider porous media in the domain.
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The reflection analysis was conducted with 2 layers as to prevent model instability in overtopping conditions. The
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study of wave transformation and the generation of boundary conditions for the Olaflow model is done with 4 layers.
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\subsubsection{Porosity}
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In the SWASH model, the porous breakwater armour is represented using macroscale porosity. The porosity parameters were
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calibrated in \textcite{poncet2021}.
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\subsubsection{Boundary conditions}
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Two different sets of boundary conditions were used for both studies. In all cases, a sponge layer was added to the
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shorewards boundary to prevent wave reflection on the boundary. In the reflection analysis, offshore conditions were
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generated using the wave spectrum extracted from buoy data during the storm. The raw vertical surface elevation
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measured by the wave buoy was used in a second part.
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\begin{figure*}
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\centering
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\includegraphics{fig/aw_t0.pdf}
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\caption{Domain studied with Olaflow. Initial configuration.}\label{fig:of}
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\end{figure*}
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\printbibliography
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\end{document}
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