The influence of the gravitational circulation on estuarine sand dune migration: an idealized modelling approach
Authors: van der Sande Wessel M. , Roos Pieter C. , Gerkema Theo , Hulscher Suzanne J. M. H. 
Published: March 2021

&lt;p&gt;Estuarine sand dunes are &amp;#8211; similar to river dunes and marine sand waves &amp;#8211; large-scale rhythmic bed patterns. Their characteristics differ from their riverine and marine counterparts, owing to the complex and dynamic estuarine environment. Using an idealized process-based modelling approach, we investigate the effect of the gravitational circulation on estuarine sand dunes.&lt;/p&gt;&lt;p&gt;The gravitational circulation is a residual current typical to estuaries, as it results from a longitudinal salinity gradient. It constitutes a tide-averaged residual flow with an upstream-directed (landward) component at the bed and a downstream-directed (seaward) component at the water surface (Geyer&amp;#160;&amp;&amp;#160;MacCready,&amp;#160;2014). Sediment transport primarily depends on the bed shear stress (and thus on the flow near the bed), and therefore this residual flow may well be responsible for upstream migration of these bedforms. Observations of sand dunes in the Gironde estuary, France, suggest that this may indeed be relevant to the migration direction of estuarine sand dunes (Bern&amp;#233; et al., 1993).&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;We incorporated the hydrodynamic features of the gravitational circulation in a morphodynamic model, which is similar to the one of Hulscher (1996). We then perform a so-called linear stability analysis, which shows that bedforms develop as free instabilities of the flat bed.&lt;/p&gt;&lt;p&gt;Results show that a longitudinal salinity gradient may cause upstream migration, provided that the river flow velocity is sufficiently small. During high discharge in the Gironde estuary, the salinity front is pushed outward (van Maanen &amp; Sottolichio, 2018), thus increasing the salinity gradient at the position in the Gironde where the sand wave field is situated. Including this in the model shows that the strengthened gravitational circulation can overpower the increased river flow velocities during high discharge, and thus confirms the observation by Bern&amp;#233; et al. (1993). We note that this mechanism is probably limited to estuaries which share similar characteristics as the Gironde estuary, i.e. symmetric tide, well-mixed, little wind and wave influence, and a small residual river flow velocity due to a significant increase in cross-sectional area. Future research will elaborate on the effects of (tidally varying) stratification through implementation of a time- and space dependent eddy viscosity.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Bern&amp;#233;, S., Castaing, P., le Drezen, E., &amp; Lericolais, G. (1993). Morphology, Internal Structure, and Reversal of Asymmetry of Large Subtidal Dunes in the Entrance to Gironde Estuary (France). Journal of Sedimentary Petrology, 63(5), 780&amp;#8211;793. https://doi.org/10.1306/d4267c03-2b26-11d7-8648000102c1865d&lt;/p&gt;&lt;p&gt;Geyer, W. R., &amp; MacCready, P. (2014). The Estuarine Circulation. Annual Review of Fluid Mechanics, 46, 175&amp;#8211;197. https://doi.org/10.1146/annurev-fluid-010313-141302&lt;/p&gt;&lt;p&gt;Hulscher, S. J. M. H. (1996). Tidal-induced large-scale regular bed form patterns in a three-dimensional shallow water model. Journal of Geophysical Research, 101(C9), 727&amp;#8211;744. https://doi.org/10.1029/96JC01662&lt;/p&gt;&lt;p&gt;van Maanen, B., &amp; Sottolichio, A. (2018). Hydro- and sediment dynamics in the Gironde estuary (France): Sensitivity to seasonal variations in river inflow and sea level rise. Continental Shelf Research, 165(May), 37&amp;#8211;50. https://doi.org/10.1016/j.csr.2018.06.001&lt;/p&gt;