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

During test T01, T02 and T03 of the 2006 Deltaflume experiment \citep{VanGent2008} the effect of the wave period on dune erosion was examined. It was found that the dune erosion volume increases for a larger wave period, which is caused by a larger flow related sediment transport. In addition, the increase in flow related sediment transport is mainly a result of a higher mean sediment concentration whereas the time and depth averaged flow velocity has the same order of magnitude within the range of wave periods examined.  
The aim of this section is to examine the processes, which cause the wave period effect in the model and to what extent these processes are in line with the mechanisms observed in the measurements. To this end test T01, T02 and T03 of the Deltaflume experiment are simulated. The simulations are performed on a regular grid with dx = 1 m and input to the model are time series of short wave varying energy (low pass filtered on the wave group time scale) and incoming (bound) long waves. The time series are constructed from pressure and flow measurements at x = 41 m from the wave board. The short wave group velocity (associated with advection of wave action) is based on the $T_{m-1,0}$ wave period. Settings for the wave energy dissipation model are found in \autoref{tab:wave_dissipation} and other setting are defaults as listed in in Appendix B in \citet{VanThielDeVries2009}. 

\begin{table}[H]
  \caption{Wave dissipation parameter settings}
  \label{tab:wave_dissipation}
  \begin{center}
    \begin{tabular}{llll}
      \hline
      Experiment & $\alpha$ & $\gamma$ & $n$ \\ 
      \hline
      T01        & 1.0      & 0.50     & 10  \\ 
      T02        & 1.0      & 0.48     & 10  \\ 
      T03        & 1.0      & 0.45     & 10  \\ 
      \hline
    \end{tabular}
  \end{center}
\end{table}

In \autoref{fig:deltaflume2006_t01_profile} to \autoref{fig:deltaflume2006_t03_profile} the simulated profile evolution during the tests compares well with the measured profile evolution. However, the bar type feature at the offshore edge of the developing foreshore is not reproduced in the simulations. Comparing measured and simulated dune erosion volumes in \autoref{fig:deltaflume2006_t01_morpho} to \autoref{fig:deltaflume2006_t03_morpho} it is seen that for test T03 the erosion volume after 1 hour and 2.04 hours of waves is underestimated whereas for test T01 and T02 simulated erosion volumes are reasonably well predicted over all test intervals.

${tools.image('Deltaflume2006/T01/', 'final_profiles.png', 'Profile development during test T01', 'deltaflume2006_t01_profile')}
${tools.image('Deltaflume2006/T02/', 'final_profiles.png', 'Profile development during test T02', 'deltaflume2006_t02_profile')}
${tools.image('Deltaflume2006/T03/', 'final_profiles.png', 'Profile development during test T03', 'deltaflume2006_t03_profile')}

${tools.image('Deltaflume2006/T01/', 'morpho.png', 'Erosion pattern and volumes and retreat distance during test T01', 'deltaflume2006_t01_morpho')}
${tools.image('Deltaflume2006/T02/', 'morpho.png', 'Erosion pattern and volumes and retreat distance during test T02', 'deltaflume2006_t02_morpho')}
${tools.image('Deltaflume2006/T03/', 'morpho.png', 'Erosion pattern and volumes and retreat distance during test T03', 'deltaflume2006_t03_morpho')}

Simulated time and depth averaged flows are compared in \autoref{fig:deltaflume2006_t01_hydro} to \autoref{fig:deltaflume2006_t03_hydro}, which shows that the mean flow slightly increases with a larger wave period (6\% between x = 170 m and x = 205 m). This tends to be a slightly different trend than observed in the measurements that show a 3\% increase in the same cross-shore area. It is remarked though that any firm conclusions cannot be made since the measured time and depth averaged flow velocities are based on limited sensors over depth (and for that reason it was concluded that the mean flows for test T01 and T03 are comparable). 

The increase in the simulated offshore directed mean flow is caused by an increase of the short wave related mass flux whereas the roller related mass flux is only slightly different. The maximum long wave related mean flow is larger during test T01 than during test T03.

${tools.image('Deltaflume2006/T01/', 'hydro.png', 'Hydrodynamics during test T01', 'deltaflume2006_t01_hydro')}
${tools.image('Deltaflume2006/T02/', 'hydro.png', 'Hydrodynamics during test T02', 'deltaflume2006_t02_hydro')}
${tools.image('Deltaflume2006/T03/', 'hydro.png', 'Hydrodynamics during test T03', 'deltaflume2006_t03_hydro')}

It is concluded that the effect of the wave period on dune erosion and dune face retreat is favourably predicted with the XBeach model. The simulated increase in dune erosion with a larger wave period is mainly caused by an increase of the mean sediment concentration of O(60\%), which is comparable to the measurements. The near dune return flow slightly increases with approximately 6\% for a larger wave period. However, the accuracy of measured time and depth averaged flows is insufficient to verify this increase.
