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

This test is absed on the Zwin breach growth experiment, as reported by \citet{Visser1998}. In the mouth of the Zwin, a tidal inlet located at the border between the Netherlands and Belgium, an artificial dam was constructed with a crest height of 3.3 m +N.A.P. (Dutch datum, approx. MSL), crest width 8 m, inner slope 1:3 outer slope 1:1.6 and length 250 m. An initial depression of 0.8 m was made in the middle of the dam having a width of 1 m and a side slope of 1:1.6 to ensure that the breach initiated at this location. The level of the surrounding sea bed was about 0.7 m + N.A.P. The mean tidal prism of the Zwin is about 350,000 m3. The polder area $A_p$ as a function of the water level behind the dam is given by:

\begin{array}{lcrclcrcrcccl}
  A_p &=& 170.000m   &\cdot& z_s &-& 100.000m^2    &,& 0.6m &\textless& zs &\textless& 2.3m + NAP \\ 
  A_p &=& 2.100.000m &\cdot& z_s &-& 4.540.000m^2  &,&      &         & zs &\ge      & 2.3m + NAP
\end{array}

At t = 0, about 10 minutes prior to high water, the water level at the seaside was 2.72m+NAP. At t = 10 minutes a water level of 2.75m+NAP. was reached. For the remainder of the test, which had a total duration of 1 hour, the water level marginally decreased. After 1 hour the breach growth became nil, as the water level of the polder area behind the breached equaled the sea level. The wave height near the dam was negligible during the experiment. The wind speed was about 2 m/s. 
Until t = 6.5 minutes the breach depth grew whereas the breach width remained constant. At t = 6.5 minutes the original dike structure had nearly completely disappeared over the initial depression width of 1 m. Near t = 6.5 minutes the onset of lateral breach growth was observed. The scour hole developed further down to a depth of -1.6m+NAP. (4.9 m below the original dam crest level). The rate of lateral breach growth was about 2 cm/s. After approximately 40 minutes the process slowed down considerably and after approximately 1 hour the water levels at both sides were equal. 
A schematized representation of the Zwin test was created in XBeach, with at the sea side a uniform bed level at 0.7m+NAP, and inside the basin a prismatic profile with the deepest point at 0.7m+NAP and sloping sides, such that the polder area as a function of the water level was in accordance with the equations above. The grid is non-equidistant with grid sizes gradually varying from 0.5 m near the breach to approx. 50 m far away from it. The median grain diameter $D_{50}$ of the bed material was set to 0.3 mm in accordance with the prototype test conditions for the artificial dam. The applied critical slopes for avalanching are the same as in other tests and standard settings were applied for the transport formulations. Waves were negligible in the test and were set to zero. The model was run with a CFL of 0.5 and remained smooth and stable despite the steep slopes and supercritical flows.

In \autoref{fig:Zwin_T01_default_fig2} a sequence of 3D images is shown depicting the various stages in the breaching process: the initial overflowing, the cutting back of the breach, the deepening and finally the widening of the breach.

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Qualitatively and quantitatively the results are in agreement with the experiment by \citet{Visser1998}, although details may be different due to the schematized initial bathymetry. 

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${tools.image('Zwin_T01/', 'fig2.eps', 'Growth of breach width')}

In \autoref{fig:Zwin_T01_default_fig1} a comparison is given between measured and simulated water levels, flow velocities and development of the breach width in time. Observation point MS2 is 30 m upstream of the centre point of the breach and MS4 is 30 m downstream of it. In MS4 there was some ambiguity in the measured initial water level, which explains the initial discrepancy between measurements and simulations.

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The slight reduction in water level at the end of the measurement in MS2 is due to a rather narrow channel that was present in reality but not in the model, which causes higher velocities than in the model and a reduction of the mean water surface. In spite of these differences, the overall agreement for the development of the velocity in MS4 and for the breach widening is quite satisfactory. Measured and simulated flow velocities compare reasonably well in MS4.

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${tools.image('Zwin_T01/', 'fig1.eps', 'Breach width related to water level and flow velocities')}