Formation of tidal sand ridges and long bed waves subject to 3D tidal flow

Abstract

Tidal sand ridges and long bed waves are rhythmic bed forms that form as a result from the interaction between the forcing of oscillatory tidal currents and the topography of the bottom. Gaining knowledge of these patterns is important for navigation and to know their response to sand mining. Tidal sand ridges are rotated cyclonically (5 − 30 degrees) with respect to the direction of the tidal current. The typical distance between successive crests is about 10 km. In contrast, crests of long bed waves can be rotated cyclonically (~60 degrees) or anticyclonically (~30 degrees) with respect to the tides and their crest-to-crest distance is about 1.5 km. Several studies have explained the initial growth and the wavelength and orientation of tidal sand ridges. However, it is unclear why the crests of cyclonic oriented long bed waves are rotated further cyclonically than the crests of tidal sand ridges. One potential explanation for that might be the necessity to account for the vertical structure of the tidal currents. In fact, this is the working hypothesis of this study. The model used in the present study extends the shallow water equations and introduces a formulation for multiple levels of water. These levels are coupled to the adjacent ones by means of considering the stresses at the interfaces. This assumption allows the vertical structure of the tidal currents to be incorporated in the model. Furthermore, the model includes a sediment transport formulation with a critical bed shear stress below which no sediment moves, as well as the presence of the elliptical tidal currents. The present work provides new insights in the initial formation of long bed waves and tidal sand ridges, though the main focus is on which tidal conditions allow long bed waves to emerge and how long bed waves form. The results of this study show that the agreement between observed and modelled long bed waves improves when the vertical structure of the tidal currents is included. In fact, the crests of modelled cyclonic oriented long bed waves rotate further cyclonically by ~25 degrees due to Ekman veering and enhanced eccentricity of the tidal ellipse near the seabed.