163 lines
5.8 KiB
TeX
163 lines
5.8 KiB
TeX
\chapter{SWASH model}
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\section{1D model}
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In order to find out if the reflection induced by the breakwater has an
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influence on the sea state at the buoy's location, a one-dimensional model of
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the zone between the buoy and the breakwater was created.
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The considered domain is \SI{1450}{\m} long, with \SI{1250}{\m} between the
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buoy and the breakwater, and a further \SI{200}{\m} offshore of the buoy.
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The model is a 10 layers swash model accounting for porous media in near the
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breakwater. The model was adapted from PA Poncet.
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\subsection{Model 1}
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A first run was produced in order to test the model with a water level of
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\SI{0.5}{\m} using the measured spectrum from 2017-02-28 as the offshore
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boundary condition and a sommerfeld radiation condition on the breakwater
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boundary. The model was run over a duration of 30 minutes.
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The same model was implemented without the breakwater (by forcing a minimum
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depth) with an added \SI{250}{\m} sponge layer at the shorewards boundary.
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The reflection coefficient at the buoy's location was computed using
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a PUV method \parencite{huntley1999use}.
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The results are displayed in \autoref{fig:swash_1_R}. Two methods of
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calculating the reflection were used \parencite{huntley1999use}, the second one
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might be wrongly implemented, and the first one might be subject to
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noise-induced bias.
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\begin{figure}
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\centering
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\includegraphics{R1.png}
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\includegraphics{R2.png}
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\caption{Reflection coefficient computed with Swash. 1: With breakwater; 2:
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Without breakwater.}\label{fig:swash_1_R}
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\end{figure}
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\subsection{Model 2}
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An attempt at running the model with the correct water level (\SI{4.5}{\m}) was
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made without success, as the model does not seem to be able to compute
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overtopping. Changing the boundary condition at the breakwater does not fix the
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issue, and the model is not able to run with water on both sides of the
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breakwater as the initial condition.
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\paragraph{SWASH overtopping} \cite{suzuki2011applicability,zhang2020numerical} It seems like computing wave overtopping
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should be possible using the SWASH model.
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Implemented model with longer domain, with water behind the breakwater; currently, model crashes when overtopping
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happens.
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The model DOES NOT crash if layers are disabled (depth-averaged model). No overtopping seems to appear in the results.
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Resulting reflection coefficient in \autoref{fig:swash_nolay}: very high reflection coefficient, probably inaccurate.
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\begin{figure}
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\centering
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\includegraphics{R_singlelayer.png}
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\caption{Reflection coefficient computed with Swash without layers (method 1, probable noise-induced
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bias.}\label{fig:swash_nolay}
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\end{figure}
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Model does also work with 2 layers; overtopping does appear \autoref{fig:swash_2lay}.
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\begin{figure}
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\centering
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\includegraphics{R_2lay.png}
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\caption{Reflection coefficient computed with Swash 2 layers (method 1, probable noise-induced
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bias.}\label{fig:swash_2lay}
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\end{figure}
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Model crashes with 3 or more layers.
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\subsection{Model 3}
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Model: \SI{1450}{\m} offshore, \SI{300}{\m} shorewards. \SI{250}{\m} sponge layer. \SI{4.5}{\m} water level. 2 layers.
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\autoref{fig:bathy}
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\begin{figure}
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\centering
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\includegraphics{bathy_b.pdf}
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\includegraphics{bathy_nb.pdf}
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\caption{Bathymetry.}\label{fig:bathy}
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\end{figure}
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Results \autoref{fig:res45}.
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\begin{figure}
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\centering
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\includegraphics{R_2lay_45.pdf}
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\caption{Results (1: breakwater; 2: no breakwater).}\label{fig:res45}
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\end{figure}
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Comparison with reflex3s (array method adapted from PA Poncet) \autoref{fig:reflex3s2lay}.
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\begin{figure}
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\centering
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\includegraphics{reflex3s_2lay.pdf}
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\caption{Reflection coefficient with array method.}\label{fig:reflex3s2lay}
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\end{figure}
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\subsection{Model with measured time-series}
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Using raw buoy data. Model crashes with 2 layers. Works when layers are disabled. \textbf{No overtopping!}
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\autoref{fig:rests}. \SI{1}{\hour} computation time.
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\begin{figure}
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\centering
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\includegraphics{R_ts.pdf}
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\caption{Results with real timeseries, no layers.}\label{fig:rests}
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\end{figure}
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Model runs with 2 layers after adjusting some parameters. \autoref{fig:rests2lay}. Overtopping is computed.
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\begin{figure}
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\centering
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\includegraphics{R_ts_2lay.pdf}
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\caption{Results with real timeseries, 2 layers.}\label{fig:rests2lay}
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\end{figure}
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Model runs with 4 layers. \autoref{fig:rests4lay}.
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\begin{figure}
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\centering
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\includegraphics{R_ts_4lay.pdf}
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\caption{Results with real timeseries, 4 layers.}\label{fig:rests4lay}
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\end{figure}
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\section{Reflection coefficient verification}
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A small Python script has been written to generate theoretical wave height and homogenized velocity for a combination of
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incident and reflected waves.
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The method was taken from \parencite{huntley1999use}. Incident waves are modelled by white noise, reflected waves are
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incident waves shifted and multiplied by the reflection coefficient. Water level is the sum of incident waves and
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reflected waves, velocity is the difference of reflected waves and incident waves. Additionnal noise is added to the
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water level and velocity.
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Results are displayed in \autoref{fig:r_test}.
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\begin{figure}
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\centering
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\includegraphics{r_test.pdf}
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\caption{Reflection coefficient testing (puv method from \cite{huntley1999use}).}\label{fig:r_test}
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\end{figure}
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\section{Plotting orbitals from buoy measurements}
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\autoref{fig:orbitals}. Orbital for the large wave have been plotted in the average motion plane of the buoy.
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\begin{figure}
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\centering
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\includegraphics{orbitals.pdf}
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\caption{2Dv buoy trajectory for wave event of 20170228.}\label{fig:orbitals}
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\end{figure}
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\subsection{Buoy spectrum}
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The swash model was run over 4 hours with the spectrum obtained from the buoy, with and without the breakwater. (2
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layers).
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A zero-crossing methods was implemented to find the largest waves.
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%\subsection{2D Model}
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%Working on 2D model which might work with overtopping.
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