Sensitivity of growth characteristics of tidal sand ridges and long bed waves to formulations of bed shear stress, sand transport and tidal forcing: A numerical model study

• A numerical model is used to simulate initial formation of tidal sand ridges and long bed waves.
• The effects of different formulations of bed shear stress, sand transport and tidal forcing on the characteristics of these bedforms are systematically examined.
• In the orientation and wavenumber space, the number of long bed waves relates to tidal ellipticity.

Tidal sand ridges and long bed waves are large-scale bedforms that are observed on continental shelves. They differ in their wavelength and in their orientation with respect to the principal direction of tidal currents. Previous studies indicate that tidal sand ridges appear in areas where tidal currents are above 0.5 m s−1, while long bed waves occur in regions where the maximum tidal current velocity is slightly above the critical velocity for sand erosion and the current is elliptical. An idealized nonlinear numerical model was developed to improve the understanding of the initial formation of these bedforms. The model governs the feedbacks between tidally forced depth-averaged currents and the sandy bed on the outer shelf. The effects of different formulations of bed shear stress and sand transport, tidal ellipticity and different tidal constituents on the characteristics of these bedforms (growth rate, wavelength, orientation of the preferred bedforms) during their initial formation were examined systematically.The results show that the formulations for bed shear stress and slope-induced sand transport are not critical for the initial formation of these bedforms. For tidal sand ridges, under rectilinear tidal currents, increasing the critical bed shear stress for sand erosion decreases the growth rate and the wavelength of the preferred bedforms significantly, while the orientation angle slightly decreases. The dependence of the growth rate, wavelength and the orientation of the preferred bedforms on the tidal ellipticity is non-monotonic. A decrease in tidal frequency results in preferred bedforms with larger wavelength and smaller orientation angle, while their growth rate hardly changes. In the case of joint diurnal and semidiurnal tides, or spring-neap tides, the characteristics of the bedforms are determined by the dominant tidal constituent. For long bed waves, the number of anticyclonically/cyclonically oriented bedforms with respect to the principal current direction increases as the ellipticity of the cyclonic/anticyclonic tidal currents increases. Besides, under anticyclonic tidal currents, the growth rate of cyclonically oriented long bed waves increases as the tidal ellipticity increases. The model was also used to provide a possible explanation for the fact that the Dutch Banks have a larger wavelength than that of the Flemish Banks in the North Sea.