# 15.18. Sandbar¶

This test case is part of an effort to develop a comprehensive 3D nearshore model that predicts onshore and offshore sandbar migrations under storm and post-storm conditions, without the need to modify the model setting parameters. In this test, we attempt to reproduce the results of sandbar migration experiments, the European Large Installation Plan (LIP) experiments, which were carried out at full scale in Delft Hydraulics’s Delta Flume (Roelvink and Reniers, 1995). Hydrostatic wave-averaged simulations of LIP-1B (erosion) and LIP-1C (accretion) using CROCO are described in Shafiei et al. (2022), while wave-resolving simulations are in Marchesiello et al. (2021) for hydrodynamics and Marchesiello et al. (2022) for morphodynamics.

In LIP, three types of experiments were carried out under different types of irregular waves, which subsequently resulted in a stable (1A), erosive (1B), and accretive (1C) beach state. The initial profile is linear in LIP-1A, with a slope of 1:30 and consisting of a median grain size of 0.22 mm. The final profile of LIP-1A was used as the initial profile of LIP-1B and the final profile of LIP-1B as the initial profile of LIP-1C. The wave conditions were a JONSWAP narrow-banded random wave spectrum with a peak enhancement factor of 3.3 and characteristic wave height and period: Hs =1.4m,Tp =5s (LIP-1B) and Hs =0.6m,Tp =8s (LIP-1C).Under this wave forcing, the sandbar developed during LIP-1B, increasing in height and migrating in the offshore direction. Under the accretive conditions of LIP-1C, the bar migration reversed to the onshore direction. For validation of currents and sand concentration, we consider the time 8 hours after initialization in experiment 1B and 7 hours in 1C. The LIP-1B and LIP-1C experiments lasted 18 and 13 hours, respectively. In both cases, the model was run for one hour with a morphological acceleration factor equal to 18 and 13 respectively.

The model can be run using wave-averaged equations in hydrostatic mode or wave-resolving nonhydrostatic equations.

## 15.18.1. Wave-averaged solution (default)¶

Here, wave-averaged equations are used that require parametrization of wave effects on morphodynamics. Bedload nonlinear wave-related transport is parametrized with the SANTOSS formulation, which follows the wave half-cycle concept to account for wave asymmetry and skewness. LIP1b and LIP1c experiments are conducted sequentially, meaning that the final bathymetry of LIP1b is the initial bathymetry of LIP1c. The numerical domain is 200 meters long and 4.1 m deep. The numerical domain is discretized using a uniform grid with horizontal resolution of 1.5 m and the number of vertical layers is 20 throughout the domain (the heights of the cells in the deep region and around the bar are about 21 cm and 5 cm respectively).

For wave forcing, CROCO is fully coupled to built-in ray-theory spectrum-peak wave propagation model. The offshore wave height is forced at the model boundary with values of the experiments. The resulting Dean number $$\Omega=H_s/T_p W_s$$ clearly differentiates the erosive and accretive conditions. Apart from the forcing conditions, all other wave model parameters are the same for both cases.

For the sediment transport model, the main calibration parameters to be tuned in the suspended load model are: the settling velocity $$W_s=25$$ mm/s; the critical bed shear stress $$\tau_{CE}=0.18 \, \text{N/m}^2$$; and erosion rate $$E_0=0.001 \, \text{kg/m}^2\text{/s}$$. For bed roughness, the bottom boundary layer model (BBL) uses empirical formulations for sand mobilization based on grain size and wave statistics. For bedload transport, SANTOSS is implemented with only one calibration parameter: the bedload factor, which is set to 0.5.

## 15.18.2. Wave-resolved solution (#define NBQ)¶

In this case, we do not rely on parametrization for the bottom boundary layer or bedload transport, as as skewed-asymmetric waves are resolved explicitly, but we make sure that the wave-boundary layer is resolved, and that the first vertical level is in a sheet flow layer (about 10 times the grain size). This is particularly important for the onshore bar migration phase. Note that in our formulation, the turbulence intensity (calculated with the closure model) affects the sediment resuspension. A numerical wave maker forces the JONSWAP spectrum of linear waves at the offshore boundary (as in the laboratory experiments).

Roelvink, J.A., Reniers, 1995. LIP 11D delta flume experiments : a dataset for profile model validation. WL / Delft Hydraulics.

Shafiei H., J. Chauchat, C. Bonamy, and P. Marchesiello, 2022: Numerical simulation of on-shore/off-shore sandbar migration using wave-cycle concept – application to a 3D wave-averaged oceanic model (CROCO), in preparation for Ocean Modelling.

Marchesiello P., J. Chauchat, H. Shafiei, R. Almar, R. Benshila, F. Dumas, 2022: 3D wave-resolving simulation of sandbar migration. Coastal Engineering, submitted.

Marchesiello P., F. Auclair, L. Debreu, J.C. McWilliams, R. Almar, R. Benshila, F. Dumas, 2021: Tridimensional nonhydrostatic transient rip currents in a wave-resolving model. Ocean Modelling, 163, 101816.

# define SANDBAR


CPP options:

# define SANDBAR_OFFSHORE /* LIP-1B */
# undef  SANDBAR_ONSHORE  /* LIP-1C */
# undef  OPENMP
# undef  MPI
# undef  NBQ
# define SOLVE3D
# define NEW_S_COORD
# define ANA_GRID
# define ANA_INITIAL
# define ANA_SMFLUX
# define ANA_STFLUX
# define ANA_SSFLUX
# define ANA_SRFLUX
# define ANA_SST
# define ANA_BTFLUX
# define OBC_WEST
# define SPONGE
# define WET_DRY
# ifndef NBQ /* ! NBQ */
#  define MRL_WCI
#  ifdef MRL_WCI
#   define WKB_WWAVE
#   define MRL_CEW
#   define WKB_OBC_WEST
#   define WAVE_ROLLER
#   define WAVE_FRICTION
#   define WAVE_BREAK_TG86
#   define WAVE_BREAK_SWASH
#   define WAVE_STREAMING
#   undef  WAVE_RAMP
#  endif
#  define GLS_MIXING
#  define GLS_KOMEGA
#  undef  LMD_MIXING
#  ifdef LMD_MIXING
#   define LMD_SKPP
#   define LMD_BKPP
#   define LMD_VMIX_SWASH
#  endif
#  define BBL
# else /* NBQ */
#  define MPI
#  define NBQ_PRECISE
#  define WAVE_MAKER
#  define GLS_MIXING_3D
#  define GLS_KOMEGA
#  define ANA_BRY
#  define Z_FRC_BRY
#  define M2_FRC_BRY
#  define M3_FRC_BRY
#  define T_FRC_BRY
#  define AVERAGES
#  define AVERAGES_K
#  define DIAGNOSTICS_EDDY
# endif /* NBQ */
# define SEDIMENT
# ifdef SEDIMENT
#  define MORPHODYN
#  define TCLIMATOLOGY
#  define TNUDGING
#  define ANA_TCLIMA
# endif
# undef  STATIONS
# ifdef STATIONS
#  define ALL_SIGMA
# endif
# undef  DIAGNOSTICS_TS
# ifdef DIAGNOSTICS_TS