Dispersion and dynamically one-dimensional modeling of salt transport in estuaries

Abstract

An estuary forms the transition between the ocean/sea and a river. Within its boundaries salt and fresh water mix. Fresh water intake points may be located within the reach of salt intrusion. In order to justify political and managerial decisions it is thus necessary to understand and be able to predict the process of salt intrusion in estuaries. Within this thesis the one-dimensional modeling suite SOBEK is used to simulate salt intrusion in estuaries. Within SOBEK the one-dimensional continuity and momentum equations are used to describe hydrodynamics within the system. A state equation, relating salinity and density, is used to couple an advection-diffusion equation to the momentum equation. This advectiondiffusion equation can be used to describe salt transport and makes use of a dispersion coefficient. The dispersion coefficient should capture the mixing mechanisms taking place in an estuary. Mixing mechanisms in an estuary are induced by tidal forcing, river discharge or wind and the most dominant ones are gravitational circulation and tidal pumping. Recent validations of SOBEK have mainly focused on water levels and discharges, while less attention was payed to its capability to describe salt transport. The objective of this research is thus to obtain a better understanding of dynamic one-dimensional modeling of salt transport, validate the model and used dispersion coefficient, determine the applicability of the model and improve the dispersion coefficient based on the latest insights and recent developments. The study is performed using two data sets. One of which is a prismatic tidal flume experiment conducted in the 60’s at Delft Hydraulics. The other one is a data set considering worldwide measurements in convergent estuaries by Savenije and his students. The nature of the considered water bodies, tidal flume and real convergent estuaries, differs much and so do the results and conclusions regarding both data sets. The first analysis performed was testing the dispersion formulation based on the one derived by Thatcher and Harleman (1972) which is currently used in SOBEK. Based on validation results for both the tidal flume experiment and real convergent estuaries and an analysis of the dispersion relation, improvements to the dispersion formulation were formulated and tested in the second phase of this research. For example, simulations for the tidal flume test showed that the model was not capable of dealing with changes in bed roughness or water depth in the tidal flume and as such terms containing those characteristics were added to the dispersion formulation. In search of a better performing dispersion formula, the effect of the improvements to the dispersion formulation are tested. Individual adjustments were tested separately on the tidal flume simulations. More recent formulations derived by Savenije (2012), Kuijper and Van Rijn (2011), Gisen et al. (2015) and Zhang and Savenije (2016) are tested on the tidal flume experiment and/or real convergent estuaries . The dispersion formulations described by those researchers all contain one or more of the suggested improvements and together they contain all of the suggested improvements. For the tidal flume experiment model results using dispersion formulas derived by Thatcher and Harleman, Gisen and Kuijper and van Rijn are compared. For convergent estuaries simulations using dispersion formulas derived by Thatcher and Harleman, Gisen, Savenije, Kuijper and van Rijn and Zhang are compared. For the tidal flume experiment the dispersion formula derived by Kuijper and van Rijn clearly performed best. This formulation relates the dispersion coefficient to the maximum flood velocity in the estuary mouth, the water depth in the estuary mouth, the estuarine Richardson number1, the bed roughness and the relative salinity. Other formulas performed worse as they do not relate dispersion with the water depth in the estuary mouth or bed roughness. For the convergent estuaries none of the assessed dispersion formulations performed substantially better than the others as all of them result in strong correlation between measurements and simulations. However, the simulations using the dispersion formula’s described by Thatcher and Harleman (1972) and Gisen et al. (2015) are closer to the measurements than the other ones. The formulas described by Savenije, Kuijper and van Rijn and Zhang underestimated the salt intrusion and may potentially be improved by recalibrating the constant used. The dispersion formulation derived by Gisen is the simplest formulation, while it performs more or less equally well than the others. Here it is therefore suggested to continue with this dispersion formula. Gisen related dispersion at the inflection point to the maximum flood velocity, the tidal excursion and the estuarine Richardson number and used the relative salinity to convert this to dispersion along an estuary. Savenije and Kuijper and van Rijn additionally included terms relating dispersion to the estuary geometry and bed roughness, however this did not lead to better results. The formulation of Thatcher and Harleman uses the estuary length, instead of the tidal excursion, as a mixing length scale. This estuary length is not well defined and lacks a physical background regarding dispersive salt transport. Therefore the formulation derived by Thatcher and Harleman is not recommended.