Modeling the finite-height behavior of offshore tidal sand ridges, a sensitivity study

Tidal sand ridges are large-scale bedforms with horizontal dimensions of several kilometers and heights in the order of tens of meters, which occur on outer shelves of coastal seas. In order to study the long-term evolution of these ridges, an idealized nonlinear numerical model was developed. With this tool, the sensitivity of the characteristics of these finite-height ridges, in particular, their shape and growth time, to 1D/2D configuration (topography varies in one/two horizontal dimensions), tidal ellipticity and critical bed shear stress for sand erosion was investigated. In the case of a 1D configuration, the root mean square height hrms of the bedforms first grows exponentially and hereafter saturates. In the end, ridges in static equilibrium are obtained, i.e., hrms remains constant. In contrast, when the configuration is 2D, ridges are found with spatially meandering crests that oscillate in time. Initially the bedforms are composed of a finite number of bottom modes. The meanders occur if bottom modes with crests normal to those of the initially preferred bedform exist, and their topographic wavenumbers are in the order of that of the preferred bedform or smaller. In addition, the vertical distance between the crest and trough levels should be larger than around 80% of the maximum water depth. Generally, the global growth time, i.e., the time at which hrms stops increasing after the exponential growth stage of the bedforms, is slightly larger for a 2D than for a 1D configuration. The ridge shapes are sensitive to the tidal ellipticity, while they are hardly sensitive to the critical bed shear stress. The global growth time varies non-monotonically with the tidal ellipticity, and it increases if the critical bed shear stress is included. Comparison between the model results and field observations suggests that the model is able to simulate the gross characteristics of the Dutch Banks and the Flemish Banks in the southern North Sea and that these ridges may still be growing.