Topographic forcing of tidal sandbar patterns for irregular estuary planforms

Abstract

Estuaries typically show converging planforms from the sea into the land. Nevertheless, their planform is rarely perfectly exponential and often shows curvature and the presence of embayments. Here we test the degree to which the shapes and dimensions of tidal sandbars depend on estuary planform. We assembled a dataset with 35 estuary planforms and properties of 190 tidal bars to induce broad-brush but significant empirical relations between channel planform, hydraulic geometry and bar pattern, and tested a linear stability theory for bar pattern. We found that the location where bars form is largely controlled by the excess width of a channel, which is calculated as the observed channel width minus the width of an ideal exponentially widening estuary. In general, the summed width of bars approximates the excess width as measured in the along-channel variation of three estuaries for which bathymetry was available as well as for the local measurements in the 35 investigated estuaries. Bar dimensions can be predicted by either the channel width or the tidal prism, because channel width also strongly depends on local tidal prism. Also braiding index was predicted within a factor of 2 from excess width divided by the predicted bar width. Our results imply that estuary planform shape, including mudflats and saltmarsh as well as bar pattern, depend on inherited Holocene topography and lithology and that eventually convergent channels will form if sufficient sediment is available.

Morphology of bar-built estuaries: relation between planform shape and depth distribution

“…Bed elevations were extracted from these bathymetries as follows. First, the estuary outline was digitised, excluding fully 20 developed saltmarshes, and subsequently a centreline was determined within this polygon (following the approach of Leuven et al, 2017). Bed elevations were collected on equally spaced transects perpendicular to the centreline of the estuary.…”

“…However, natural estuaries deviate from the ideal ones as result of varying degree of sediment supply, lack of time for adaptation and sea-level rise (Townend, 2012;de Haas et al, 2017) and locations wider than ideal are filled with tidal bars (Leuven et al, 2017) (Fig. 1).…”

“…It therefore seems likely that such a relation between the horizontal and vertical dimensions exists for sandy estuaries, but this is not reported in literature. Morphological models can simulate 3D bed-levels with considerable accuracy Roelvink, 2008, 2012;Braat et al, 2017), but these models are computationally intensive and need calibration and specification of initial and boundary conditions. To study unmapped systems with limited information, it would be useful to be able to estimate bed-level distributions 30 from planform geometry.…”

“…Previously, we showed in Leuven et al (2017) how locations and widths of tidal bars can be predicted from the excess width, which is the local width of the estuary minus the ideal estuary width. The summed width of bars in each cross-section was found to approximate the excess width.…”

“…Excess width is defined as the local width minus the ideal width, which is given by: in which x is the distance from the mouth, W m the width of the mouth, e is ≈ 2.7 and L W is the width convergence length (Davies and Woodroffe, 2010), which can be obtained conservatively from a fit on the width of the mouth and the landward river width (Leuven et al, 2017):…”