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

This model test, described in \citet{Arcilla1994} (2E), concerns extreme conditions with a raised water level at 4.6m above the flume bottom, a significant wave height, $H_{m0}$, of 1.4m and peak period, $T_p$, of 5s. Bed material consisted of sand with a $D_{50}$ of approximately 0.2mm. During the test substantial dune erosion took place.

Based on the integral wave parameters $H_{m0}$ and $T_p$ and a standard Jonswap spectral shape, time series of wave energy were generated and imposed as boundary condition. Since the flume tests were carried out with first-order wave generation (no imposed super-harmonics and sub-harmonics), the hindcast runs were carried out with the incoming bound long waves set to zero as well. Active wave reflection compensation (ARC) was applied in the physical model, which has a result similar to the weakly reflective boundary condition in XBeach, namely to prevent re-reflecting of outgoing waves at the wave paddle (offshore boundary).

A grid resolution of 1m was applied and the sediment transport settings were set at default values. For the morphodynamic testing the model was run for 0.8 hours of hydrodynamic time with a morphological factor of 10, effectively representing a morphological simulation time of 8 hours.  

In \autoref{fig:deltaflumelip11d_2e_hydro} the hydrodynamic results are shown for first order wave generation (as in the flume tests).

${tools.image('DeltaflumeLIP11D/2E/', 'hydro.eps', 'Hydrodynamics during test 2E', 'deltaflumelip11d_2e_hydro')}

In \autoref{fig:deltaflumelip11d_2e_morpho} the horizontal distribution of sedimentation and erosion after 8 hours is shown, and the evolution in time of the erosion volume and the dune retreat. Noteworthy is the episodic behaviour of the dune erosion, both in measurements and model. An important conclusion for physical model tests is that for dune erosion it does make a difference whether first-order or second-order wave steering is applied.

${tools.image('DeltaflumeLIP11D/2E/', 'morpho.eps', 'Morphodynamics during test 2E', 'deltaflumelip11d_2e_morpho')}

A key element in the modelling is the avalanching algorithm; even though surfbeat waves running up and down the upper beach are fully resolved by the model, without a mechanism to transport sand from the dry dune face to the beach the dune face erosion rate is substantially underestimated. The relatively simple avalanching algorithm implemented, whereby an underwater critical slope of 0.3 and a critical slope above water of 1.0 are applied, proves to be quite successful in representing the retreat of the upper beach and dune face. In \autoref{fig:deltaflumelip11d_2e_final_profiles'} the measured and modelled bed evolution are shown.

${tools.image('DeltaflumeLIP11D/2E/', 'final_profiles.eps', 'Profile development during test 2E', 'deltaflumelip11d_2e_profile')}

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We see reasonable agreement of the hydrodynamics. The low-frequency waves are slightly over estimated, while the high-frequency waves are slightly underestimated. Near the dune toe the flow velocities are overestimated.

The morphological response is well predicted. The retreat distance is computed accurately, indicating that the relatvively simple avalanching routine performs well. The total erosion volumes are slightly overestimated due to the differences in shape of the erosion profile. The measurements show a gradual transition between the profile above sturge level and below surge level, whereas XBeach shows a more sudden transition. The difference is probably due to the fixed avalanching slopes for dry and wet areas implemented in XBeach.

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