A new analytical framework for tidal propagation in estuaries

Abstract

The ultimate aim of this thesis is to enhance our understanding of tidal wave propagation in convergent alluvial estuaries (of infinite length). In the process, a new analytical model has been developed as a function of externally defined dimensionless parameters describing friction, channel convergence and river discharge. This model has been used to investigate the potential influence of human interventions such as dredging, land reclamation, and freshwater withdrawal on tidal dynamics. The method allows to reproduce the most relevant features of the tidal wave (tidal amplitude, velocity amplitude, wave celerity and phase lag) along the estuary with a minimum requirement of information, such as geometrical data and the tidal forcing at the estuary mouth. Analytical solutions to the one-dimensional St. Venant equations for tidal hydrodynamics in convergent alluvial estuaries with negligible river discharge can be cast in the form of a set of four implicit dimensionless equations for phase lag, velocity amplitude, damping, and wave celerity, as a function of two localized parameters describing friction and convergence (dependent on tidal amplitude and depth). This method allows comparison of different analytical approaches by rewriting the different solutions in the same format. In this thesis, both classical and more recent formulations are compared, showing the differences and similarities in view of their specific simplifications. The envelope method that subtracts envelopes at high water and low water can be used to derive damping equations that use different friction approximations, resulting in as many analytical solutions, and thereby building one consistent theoretical framework. It is important to note that a multi-reach approach has to be adopted to follow variations of the estuarine amplitude and depth along the estuary by simple integration of the damping over a distance interval (e.g., 1 km), which is repeated for the entire length of the estuary. The asymptotic behaviour of tidal damping has also been investigated. A new asymptotic solution of the tidal amplitude has been found that reflects the balance between friction and channel convergence when the distance from the mouth approaches infinity. As a consequence, the usual assumption that the tidal amplitude and velocity amplitude along the estuary axis can be described by an exponential function appears only to be valid for an ideal or frictionless estuary. We also found that tidal amplification is increased with deepening until a maximum value is reached at a critical depth (corresponding to the maximum tidal amplitude). A further increase of depth reduces the tidal amplification until the frictionless standing wave system is reached asymptotically. The theoretical framework has subsequently been extended to take into account the effect of river discharge, which allows the analytical solutions to be applicable even in the upstream part of an estuary where the influence of river discharge is not negligible. It is observed that the residual water level slope resulting from asymmetric friction has substantial influence on tidal wave propagation when including the effect of river discharge. The application to the Modaomen and Yangtze estuaries indicates that the proposed model fits the observations with realistic roughness values upstream, while a model with negligible river discharge can be made to fit observations only with unrealistically high roughness values. The new hydrodynamics model is particularly useful in combination with a salt intrusion model because the coupling reduces the number of calibration parameters and subsequently strengthens the reliability of the salt intrusion model. The application in 6 Malaysian estuaries shows good correspondence between the computed tidal excursion with observed salinities. Conversely, if observed salinities are known, the hydraulic parameters (depth, friction) may possibly be estimated via an inverse model using observed tidal excursion and tidal amplitudes. In summary, the new framework for analytical solutions of the tidal hydrodynamics equations is more accurate than the explicit analytical model based on the Lorentz linearization. It has been expanded to include river discharge and the effect of variable depth, and it has been coupled with an analytical salt intrusion model. This analytical framework has been proved to perform well in a wide range of estuaries where it has direct value in allowing the assessment of the consequence of human interventions, such as by dredging or water abstractions. More importantly, it provides direct insight in cause-effect relations which are often nonlinear and it is a valuable educational tool to give insight into the inner functioning of a complex hydrodynamic system.