From acfb2ee382b5aa8a7a23b358ad7374e69ed4022e Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Tue, 28 Jun 2022 15:05:11 +0200 Subject: [PATCH] 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}