Scale-dependent characteristics of equilibrium morphology of tidal basins along the Dutch–German North Sea Coast

Abstract

Tidal basins can be characterized by two major morphological elements: tidal channels and tidal flats. Some scale-dependent empirical relations have been suggested based on observations in tidal basins of the Dutch and German coast. Thus, the dimensional parameters of channel area and volume are proportional to the 1.5 power of the basin area and tidal prism, respectively, whereas the dimensionless parameters of relative channel area and the ratio between channel volume and tidal prism are both proportional to the square root of basin area (Ab). The values of the coefficients before the power in these relations are of the order of 10− 5. In order to provide physical explanations for these relations, a theoretical model and a two-dimensional horizontal numerical model are developed. Based on the concept of uniform equilibrium channel velocity, the channel cross-sectional area is directly proportional to Ab and, when integrating the cross-sectional area in the flow direction, a 1.5 power relationship between the channel volume and Ab is obtained. Due to the parameters expressing the characteristic basin depth and the ratio of channel depth to the characteristic depth, which are confirmed to be scale-insensitive in both the numerical model and in field observations, the channel area is also proportional to Ab1.5. Theoretical expressions suggest the same order for the coefficients before the power as found in empirical studies. In the numerical model, the same type of scaling relations are illustrated, and the morphological response of changing grain size and tidal amplitude can be successfully predicted by the theoretical model.