Tidal sand bar dimensions and shapes in estuaries

Estuaries show dynamic patterns of channels and bars, which are also valuable habitats, while channels provide access to harbours. In contrast with bars in rivers, we still lack explanations, theory and classifications for bars in estuaries. Theories for river bars show bar properties to be strongly dependent on channel width-to-depth ratio. For estuaries, only two physics-based theories are available. One predicts bar length to increase with flow velocity and tidal excursion length and the other with flow velocity and estuary width. However, these theories have not been tested for lack of data and experiments. Our objective is to determine bar shape and dimensions in funnel shaped alluvial estuaries and to provide predictive relations for bar shapes and dimensions. We present a new dataset measured in imagery and bathymetry with bar lengths spanning from centimetres (in experiments) to tens of kilometres. We visually identified and classified 190 bars and measured their width, length, height and number of cross-cutting barbs channels. Estuarine geometry and tidal characteristics were obtained from available databases and literature. We found that many compound bars can be seen as simple linear bars partly cut by barb channels, where partitioning of bar width collapses the data of bar length-to-width ratio. This is in agreement with the transverse wave form of bars assumed in linear stability theories that are supported by data in fluvial and coastal environments. Our empirical trend shows that sand bars in estuaries have similar length-to-width ratios as river bars but are more elongated. This trend was also found to hold for bars in numerical models and scaled laboratory experiments. Bar height is linearly related to local water depth. Natural bar length, bar width and braiding index are strongly correlated to estuary width. This relation is also evident in published data of bars in rivers and numerical models of rivers. The theoretical braiding index of tidal bars indeed depends on local width-to-depth ratio and is reasonably well predicted for our dataset. However, the theoretical models for tidal bar wave length and width surprisingly lack this correlation with estuary width and overpredict by an order of magnitude, pointing at a need to revisit tidal bar theory. The empirical relations provide a means of estimating bar dimensions when limited data are available and in order to evaluate results from numerical models and physical experiments.