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

Test DP01 and DP02 were conducted with a double-peaked wave spectrum to investigate what (spectral) wave period is best qualified to describe dune erosion \citep{VanGent2008}. In this document the tests are discussed to obtain further insight in the capability of the model to simulate dune erosion for various wave spectra. The simulations are performed on a regular grid with dx = 1m 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_DP}.

\begin{table}[H]
  \caption{Wave dissipation parameter settings}
  \label{tab:wave_dissipation_DP}
  \begin{center}
    \begin{tabular}{llll}
      \hline
      Experiment & $\alpha$ & $\gamma$ & $n$ \\ 
      \hline
      DP01       & 1.0      & 0.50     & 10  \\ 
      DP02       & 1.0      & 0.48     & 10  \\ 
      \hline
    \end{tabular}
  \end{center}
\end{table}

Simulated and measured profile evolution and dune erosion volumes for test DP01 and DP02 are compared in \autoref{fig:deltaflume2006_dp01_profile} to \autoref{fig:deltaflume2006_dp02_morpho} respectively. For test DP01 the profile evolution is accurately reproduced and results for test DP02 are reasonable even though the erosion rate during the last interval is overestimated. 

${tools.image('Deltaflume2006/DP01/', 'DP01_profiles.eps', 'Profile development during test DP01', 'deltaflume2006_dp01_profile')}
${tools.image('Deltaflume2006/DP02/', 'DP02_profiles.eps', 'Profile development during test DP02', 'deltaflume2006_dp02_profile')}

${tools.image('Deltaflume2006/DP01/', 'DP01_morpho.eps', 'Erosion pattern and volumes and retreat distance during test DP01', 'deltaflume2006_dp01_morpho')}
${tools.image('Deltaflume2006/DP02/', 'DP02_morpho.eps', 'Erosion pattern and volumes and retreat distance during test DP02', 'deltaflume2006_dp02_morpho')}

The imposed double-peaked wave spectra affect the time scale and amplitude of the simulated wave groups. Consequently, the interaction of simulated long waves with the short wave groups is different and hydrodynamics in front of the dune face are expected to have other characteristics. In \autoref{fig:deltaflume2006_dp01_hydro} and \autoref{fig:deltaflume2006_dp02_hydro} the simulated wave transformation, flows and sediment concentrations are favourably compared with measurements obtained during test DP01. It seems the model is capable to take into account the effect of various wave spectra on near dune hydrodynamics and sediment transports.

${tools.image('Deltaflume2006/DP01/', 'DP01_hydro.eps', 'Hydrodynamics during test DP01', 'deltaflume2006_dp01_hydro')}
${tools.image('Deltaflume2006/DP02/', 'DP02_hydro.eps', 'Hydrodynamics during test DP02', 'deltaflume2006_dp02_hydro')}

It is concluded that the effect of the wave spectral shape on dune erosion and dune face retreat is favourably predicted with the model. The time averaged simulated wave transformation, flow and sediment concentration compare well with the mobile frame measurements obtained during test DP01. 

In \citet{VanGent2008} the spectral mean wave period $T_{m-1,0}$ is argued to be more qualified to describe dune erosion than the peak wave period $T_p$. The simulations presented in this subsection are performed with the $T_{m-1,0}$ wave period and show satisfying results suggesting the spectral mean wave period proposed by \citet{VanGent2008} is indeed a good measure to describe dune erosion. It is remarked though that any firm conclusion would require extra simulations in which the peak wave period $T_p$ is applied instead of the $T_{m-1,0}$ wave period. In addition this would demand for a new model optimization and most likely different settings for the wave dissipation model.

${tools.image('Deltaflume2006/DP01/', 'DP01_velocity.eps', 'Velocities during test DP01', 'deltaflume2006_dp01_vel')}
${tools.image('Deltaflume2006/DP02/', 'DP02_velocity.eps', 'Velocities during test DP02', 'deltaflume2006_dp02_vel')}