Modelling sand wave-induced form roughness: The complexity of a tidal setting

Tidal sand waves are abundantly present in tide-dominated sandy shelf seas, such as the Dutch North Sea. They exhibit different characteristics (wavelengths of 100-1000 m, heights of 1-10 m, and migration rates of 1-10 m/yr; van Dijk & Kleinhans,2005). Yet, bedform information is generally not considered in basin-scale hydrodynamic models, such as the Dutch Continental Shelf Model (DCSM) of the North Sea. The grid sizes of such models are too coarse to resolve individual sand waves. However, the presence of sand waves may be implicitly included in the roughness coefficient (i.e., form roughness), which would introduce a more realistic and physics-based element into these kind of models. Instead, the bed roughness of these models is obtained from calibration against observations of tidal sea surface elevation (Zijl et al., 2023), leading to large differences in bed roughness in space, which lack a physical explanation.

Form roughness parametrizations have been widely studied in river settings for river dunes and ripples (Lefebvre & Winter, 2016; van Rijn, 1993). However, the tide, unlike a unidirectional flow, is characterised by several constituents, each expressed in terms of an amplitude and a phase. Thus, the study of form roughness in a tidal setting demands a more refined analysis than in a fluvial (unidirectional) setting.