Modelling form roughness induced by tidal sand waves
Laura Portos-Amill
Tidal sand waves are rhythmic bedforms found in tide-dominated sandy shelf seas. They are characterised by wavelengths of the order of hundreds of metres, heights of several metres, and migration rates of up to 10 m/yr (van Dijk & Kleinhans, 2005). As shown in Figure 1 for the Dutch North Sea, sand wave fields found on shelf seas vary in characteristics (e.g., wavelength, height, mean water depth).
Figure 1: Bathymetric chart of the Netherlands Continental Shelf, highlighting three regions with different bed topography: (a,b) sand waves with different characteristics, (c) no sand waves. Note the different scale of the colour bars. Data from the Netherlands Hydrographic Service.
Existing sand wave studies generally focus on the sand wave formation stage and subsequent morphodynamic evolution, but the effects of sand waves on larger-scale hydrodynamics remain unknown. Knowledge on such effects is needed because basin-scale hydrodynamic models, such as the Dutch Continental Shelf Model (DCSM, Grasmeijer et al., 2022), use grid sizes that are too coarse to resolve sand waves. Thus, in these models the effects of sand waves can only be included through the user-prescribed bed roughness. Currently, however, these models do not consider any bedform-related information for the bed roughness. Instead, a spatially non-uniform value for the bed roughness is obtained from a calibration of the sea surface elevation (Zijl et al., 2023).
Our objective is to obtain parametrisations on the form roughness that bedforms exert on the tidal flow. The depth-integrated flow over a sand wave field (with grain roughness) is compared with that over a flat bed (with an increased ‘effective’ roughness). The additional value needed for the roughness such that both flow signals have the same amplitude or phase is then the form roughness, i.e.,
form roughness = effective roughness – grain roughness .
Importantly, this leads to two form roughness values, amplitude-based and phase-based, which are not necessarily identical. Previous studies had used this superposition of different roughness contributions (van Rijn, 1993; Lefebvre & Winter, 2016), but they have always considered an instantaneous unidirectional flow (e.g., over river dunes or ripples), instead of the bidirectional tidal flow. This study is the first to consider form roughness in a tidal setting.
Results show that higher and shorter sand waves generate a higher form roughness (Figure 2). Notably, both criteria (amplitude- and phase-based) give the same qualitative behaviour, but different orders of magnitude, which highlights the complexity of considering form roughness in a tidal setting. The resulting form roughness with the phase-based criterion is of the same order of magnitude as the grain roughness, proving the importance of considering the effects of bedforms on the flow.
Figure 2: Form roughness obtained with Delft3D simulations in terms of (a) sand wave height (h_sw ) and (b) wavelength (λ_sw ). Thin black line corresponds to the grain roughness. Note the different vertical axes.
We hope that these results can be of use for modelers, and that in the future, bedform characteristics can be taken into account when prescribing the roughness values of basin-scale models, such that a more realistic representation of the processes affecting the tidal flow is attained.
References:
Grasmeijer, B., Huisman, B., Luijendijk, A., Schrijvershof, R., Van Der Werf, J., Zijl, F., De Loof, H., & De Vries, W. (2022). Modelling of annual sand transports at the Dutch lower shoreface. Ocean & Coastal Management, 217, 105984.
Lefebvre, A., & Winter, C. (2016). Predicting bed form roughness: the influence of lee side angle. Geo-Marine Letters, 36, 121-133.
Van Dijk, T. A., & Kleinhans, M. G. (2005). Processes controlling the dynamics of compound sand waves in the North Sea, Netherlands. Journal of Geophysical Research: Earth Surface, 110(F4).
Van Rijn, L. C. (1993). Principles of sediment transport in rivers. Estuaries and Coastal Seas. Aqua Publications.
Zijl, F., Zijlker, T., Laan, S., & Groenenboom, J. (2023). 3D DCSM FM: a sixth-generation model for the NW European Shelf. Technical report, Deltares 2023.
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