Tidal bars are repetitive estuarine bedforms with heights of several meters and wavelengths in the order 1–15 km. Understanding their formation and sensitivity to changes in channel characteristics is important as they hamper marine traffic and play a crucial role in the local ecosystem. Recent observations suggest that the local width of the channel is dominant in determining the tidal bar wavelength. However, theoretical studies could not reproduce the sensitivity of the tidal bar wavelength to channel width. This discrepancy between theory and observations suggests that a mechanism is missing. In this study, one of the theoretical models is extended and results in tidal bar wavelengths, lateral mode numbers, and growth rates that agree fairly well with those of natural tidal bars, including the wavelengths dependency on estuary width. An important extension of the model concerns the bed slope induced diffusive suspended load transport of sediments. With this, it is explained why previously, the modelled tidal bar wavelengths depend only weakly on estuary width and why in the extended model it does. This has, from a modelling point of view, general implications for morphological models using a total load sediment transport formulation with a so-called bed slope parameter.

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Tidal bars are noticeable features in many estuaries. Understanding their dynamic formation is important as they hamper ships and they play a crucial role for the ecosystem. This study is concerned with the key factors that determine the length of the (free) tidal bars. Observations in Dalrymple and Rhodes (1995) and by Leuven et al. (2016) showed a correlation between the tidal bar length and estuary width. Models studies by Seminara and Tubino (2001) and Schramkowski et al. (2002) showed that, initially, the tidal bars can only occur when the width-todepth ratio, the friction parameter and the tidal current amplitude exceed a certain critical value. Schramkowski et al. (2002) also suggested that for wider channels, the tidal excursion length is an important scale in determining the tidal bar length. Hibma et al. (2004) compared the results from a complex numerical model to the idealised models of Schramkowski et al. (2002) and Seminara and Tubino (2001) and suggested that the estuary depth influences the tidal bar length. From these studies not clear answer emerges on the question: ‘what internal length scale determines the tidal bar length?’. The aim is therefore to bridge the gap between different models and observations by building on, and extending previous model work. @en