\chapter{Laboratory experiments: hydrodynamics}
\label{sec:Hydrodynamics}

The hydrodynamics form the basis for the morphodynamic behaviour. In this chapter the hydrodynamic results of XBeach are presented. All tests are run without the morphological module and the analysis is focused on the wave propagation and transformation computed by XBeach.

First, two analytical solutions are reproduced by XBeach. Subsequently, laboratory experiments of a barred beach and gentle sloping beach are presented. For the latter, the short-wave height, infragravity-wave height and setup are compared to the measurements. 


The observed wave height is computed on the basis of the energy density spectrum in the frequency range of $f_p/2$ until the Nyquist frequency,
\begin{equation}
	H_{m0,HF} = 4\sqrt{m_{0,f>f_p/2}}
\end{equation} 
Where $m_{0,f>f_p}$ is the zero-moment of the energy density spectrum where the frequency is larger than the cutoff-frequency ($f_p/2$). In XBeach, the short wave height is computed as,
\begin{equation}
	H_{m0,HF} = \text{rms}(H)\sqrt{2}
\end{equation} 
where $H$ is the computed instantaneous short-wave height, which is computed in XBeach as we do not directly simulate the wave height. The infragravity-wave height in both the observations and the computations is defined as,
\begin{equation}
	H_{m0,HF} = 4\sqrt{m_{0,f_p/20<f<f_p/2}}
\end{equation} 
where $m_{0,f_p/20<f<f_p/2}$ is zero-moment of the energy density spectrum for energy in the infragravity region. Since  XBeach also resolves the infragravity waves, the same definition is applied to compute the infragrvaity wave height from the XBeach results. 

Similar as the infragravity wave height, both the observed and computed mean water level (setup) can be computed with the same formulation,
\begin{equation}
	\text{setup} = \text{mean}(\eta)
\end{equation} 
where $\eta$ is the surface elevation signal.

\section{Long wave propagation}
<%include file="longwavepropagation.tex"/>

\section{1D wave runup (analytical solution)}
<%include file="carriergreenspan.tex"/>

\section{High- and low-frequency wave transformation over a barred beach}
<%include file="boers_SB.tex"/>

\section{High- and low-frequency wave transformation over a gentle sloping beach}
<%include file="GLOBEX_SB.tex"/>

