Reversing tidal flow and estuarine morphodynamics in the Metronome laboratory flume

Our objective is to test a novel experimental principle for creating reversing tidal flows of sufficient strength to cause estuarine morphodynamics. The study of estuarine morphodynamics has hitherto been limited to field observation and numerical modelling, whilst fluvial morphodynamics have additionally been studied by scale experiments with the same sediment mobility as the prototype, here defined by the Shields number. The most important reason is the difficulty of downscaling sediment size (Kleinhans et al., 2014). The reduction of length scales, including water depth but excluding bed sediment particle size, requires a much steeper surface gradient for the same sediment mobility (Figure 1). For river scale experiments a sufficient gradient of 0.01 m/m has no other side effect than causing the flow to be critical, as is the case in natural gravel-bed rivers (Kleinhans et al., 2014). However, driving the bidirectional tidal flow in a 2 cm deep channel from the seaward boundary means that the sufficient gradient is only attained over a length of 1-2 m. Given typical channel aspect ratios of 50, this would result in a tidal channel length of the same order as channel width, which is a short tidal basin but not an estuary. Past attempts to overcome this problem forced higher tidal amplitudes which led to ebb-dominated systems (Reynolds 1887) and low-density sediments with tidal long periods in very large setups (Stefanon et al. 2010, Tambroni et al. 2005). In a recent invention, on the other hand, tidal flows with sufficient mobility were obtained in an experimental flume that periodically tilts on the short axis (Kleinhans et al. 2015). This drives the flow by gradient whilst the water surface remains approximately parallel to the bed surface as in a rigid lid approach (Figure 1). Here we test the tilting principle by flow measurement in a straight flume with rough bed. Furthermore we show how estuaries with typical convergent shapes form in cohesionless sand with an initially straight river, where estuary length depends on tidal tilting period. We use a novel tidal flume setup of 20 m length by 3 m width, the Metronome (http://www.uu.nl/metronome, Figure 2). To measure flows over a rough bed that is periodically tilting, we covered the flume with artificial grass with leaves of 14 mm high, kept submerged with medium sand. We applied 15 and 30 s tilting at 0.01 m/m gradient amplitude at an average water depth of about 30 mm. This was done for situations with two boundaries kept at constant head and with one boundary as such and the other closed off. We also ran periodic 30 and 60 s Reynolds-type tidal conditions with 20 mm amplitude at the seaward boundary. Floating particles of 3 mm diameter were seeded and imaged at 25 Hz with 7 overhead color cameras of 2048x2048 pixels. Surface flow velocity was determined by a correlation method using the matlab PMIV toolbox made available by Nobuhito Mori (2009). For comparison, we also ran a one-dimensional numerical model for the shallow water equations, with constitutive relations for submerged vegetation roughness and with bed tilting included. Results show that flow velocity is sufficient for sediment transport in the tilting experiments along most of the flume length, but decays rapidly from the seaward boundary in the Reynolds-type experiments (Figure 3). Measured velocity in the tilting experiments reduces towards the closed boundary as expected and shows a reflection in both experiment and numerical model. Near the open seaward boundary measured velocity also reduces which is unexpected and not yet understood. Furthermore the data show some reflection, possibly on the constant head weir. Regardless of these intricacies the tilting method is clearly suitable to drive reversing tidal currents and sediment transport. Subsequently, we created 10 experimental estuaries with 15-45 s tilting period, 0.005-0.015 m/m tilting gradient amplitude, with and without river inflow and oblique angle, paddle-generated waves in the sea of 1 cm high and 0.5 s period, as well as control experiments with waves or river only conditions and the Reynolds method. The experiments were recorded by timelapse overhead imaging and AGIsoft DEMs of the final bed elevation. In tilting mode, tidal currents are capable of transporting sediment in both the ebb and flood phase because they are caused by periodic tilting of the flume (example in Figure 2). In the classic method of water level fluctuation there is almost no sediment mobility. Absence of river inflow leads to short tidal basins whereas even a minor discharge leads to long convergent estuaries. Estuary width and length as well as morphological time scale over thousands of tidal cycles strongly depend on tidal current amplitude. Waves subdue the ebb delta causing stronger tidal currents in the basin. Bar length-width ratios in estuaries are slightly larger to those in braided rivers in experiments and nature. Mutually evasive ebb- and flood-dominated channels are ubiquitous and appear to be formed by an instability mechanism with growing bar and bifurcation asymmetry. Future experiments will include mud flats and live vegetation. References Kleinhans, M.G., W.M. van Dijk, W.I. van de Lageweg, D.C.J.D. Hoyal, H. Markies, M. van Maarseveen, C. Roosendaal, W. van Weesep, D. van Breemen, R. Hoendervoogt and N. Cheshier (2014), Quantifiable effectiveness of experimental scaling of river- and delta morphodynamics and stratigraphy, Earth-Science Reviews 133, 43-61, http://dx.doi.org/10.1016/j.earscirev.2014.03.001 Kleinhans, M.G., R. Terwisscha van Scheltinga, M. van der Vegt and H. Markies (2015), Turning the tide: growth and dynamics of a tidal basin and inlet in experiments, J. of Geophys. Res. Earth Surface 120, 95-119, http://dx.doi.org/10.1002/2014JF003127 Malverti, L., E. Lajeunesse, and F. Metivier (2008), Small is beautiful: Upscaling from microscale laminar to natural turbulent rivers, J. Geophys. Res., 113, F04004, doi:10.1029/2007JF000974. Reynolds, O. (1887), On certain laws relating to the regime of rivers and estuaries and on the possibility of experiments on a small scale, pp. 555–562, Br. Assoc. Rep., London. Stefanon, L., L. Carniello, A. D’Alpaos, and S. Lanzoni (2010), Experimental analysis of tidal network growth and development, Cont. Shelf Res., 30, 950–962, doi:10.1016/j.csr.2009.08.018. Tambroni, N., M. Bolla Pittaluga, and G. Seminara (2005), Laboratory observations of the morphodynamic evolution of tidal channels and tidal inlets, J. Geophys. Res., 110, F04009, doi:10.1029/2004JF000243. Yalin, M. (1971), Theory of Hydraulic Models, 266 pp., Macmillan, London. Acknowledgements: this research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs. The Metronome was designed and built in collaboration with Consmema (steel construction), Variodrive (motion), Stemmer Imaging (imaging system), Bart Boshuizen (TU-Delft, programming), and Paul Vrijbergen (UU, lab fundament and roof).