<%namespace name="tools" file="tools.tex"/>

In the \cite{Noorloos2003} experiment bichromatic waves on a plane beach are studied. A 40 meter long flume with a 1/35 slope sloping beach is used. At 80 locations the water level was measured. The waves are generated with a piston type of wave board which includes second order wave steering. Eight different bichromatic  waves are studied with varying frequency and amplitude. In this report test A1, A4 and B4 are simulated with XBeach. In test A1 most of the low frequency waves are dissipated whereas in test A4 most of the low frequency waves are reflected. Additionally, B4 is modelled, because this test contains the largest amplitude of the bound long wave. In table \ref{table:vanNoorloos} an overview of the three tests is given. The model is forced with a time series of these bichromatic waves including the second order bound waves (super and sub-harmonics). 

\begin{table}[H]
\centering
\caption{Wave conditions for the three tests \citep{Noorloos2003} which are modelled with XBeach. $f_1$ and $f_2$ are the primary wave frequency, $f_b$ is the bound wave frequency and $kd$ the maximum normalized water depth}
\label{table:vanNoorloos}
\begin{tabular}{*{7}{l}}
\hline \hline
Test &  $f_1$ (Hz) & $f_2$ (Hz) & $f_b$ (Hz) & $a_1$ (m) & $a_2$ (m) & $kd$\\ \hline
A1 & 0.67  & 0.48 & 0.19 & 0.06 & 0.012 & 2.00\\ 
A4 & 0.62  & 0.53 & 0.09 & 0.06 & 0.012 & 1.81\\ 
B4 & 0.65  & 0.50 & 0.15 & 0.06 & 0.036 & 1.95\\ \hline
\end{tabular}
\end{table}

To show the generation of the bound long wave, the time series is filtered by applying a band filter. The filter is applied to all the higher components of the difference frequency ($m\Delta f = m(f_1 - f_2)$). In this way the higher harmonics of the bound waves are included.
In figures \ref{fig:VanNoorloos_A1_A1}, \ref{fig:VanNoorloos_A4_A4} and \ref{fig:VanNoorloos_B4_B4} the results for  respectively test A1, A4 and B4 are plotted. The upper panel shows the total wave height and the lower panel the filtered bound long wave. An overview of the statistical scores is given in \autoref{tab:VanNoorloos}.

${tools.image('VanNoorloos/A1/', 'A1.eps', 'The upper panel shows the measured (blue dots) and modeled (red line) total wave height. The lower panel shows the filtered bound long wave of the measurements (blue dots) and the XBeach results (red line).')}
${tools.image('VanNoorloos/A4/', 'A4.eps', 'The upper panel shows the measured (blue dots) and modeled (red line) total wave height. The lower panel shows the filtered bound long wave of the measurements (blue dots) and the XBeach results (red line).')}
${tools.image('VanNoorloos/B4/', 'B4.eps', 'The upper panel shows the measured (blue dots) and modeled (red line) total wave height. The lower panel shows the filtered bound long wave of the measurements (blue dots) and the XBeach results (red line).')}

${tools.table('VanNoorloos/', 'skill.tex', 'Statistical scores for Van Noorloos experiments', 'VanNoorloos_nh')} 