Huayang Cai

A new analytical framework for assessing the effect of sea‐level rise and dredging on tidal damping in estuaries

This paper explores different analytical solutions of the tidal hydraulic equations in convergent estuaries. Linear and quasi-nonlinear models are compared for given geometry, friction, and tidal amplitude at the seaward boundary, proposing a common theoretical framework and showing that the main difference between the examined models lies in the treatment of the friction term. A general solution procedure is proposed for the set of governing analytical equations expressed in dimensionless form, and a new analytical expression for the tidal damping is derived as a weighted average of two solutions, characterized by the usual linearized formulation and the quasi-nonlinear Lagrangean treatment of the friction term. The different analytical solutions are tested against fully nonlinear numerical results for a wide range of parameters, and compared with observations in the Scheldt estuary. Overall, the new method compares best with the numerical solution and field data. The new accurate relationship for the tidal damping is then exploited for a classification of estuaries based on the distance of the tidally averaged depth from the ideal depth (relative to vanishing amplification) and the critical depth (condition for maximum amplification). Finally, the new model is used to investigate the effect of depth variations on the tidal dynamics in 23 real estuaries, highlighting the usefulness of the analytical method to assess the influence of human interventions (e.g. by dredging) and global sea-level rise on the estuarine environment.

Asymptotic behavior of tidal damping in alluvial estuaries

Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel, reflecting the balance between friction and channel convergence. Subsequently, explicit expressions for the tidal amplitude and velocity amplitude are derived, which are different from the generally assumed exponential damping equation that follows from linearizing the friction term. Analysis of the asymptotic behavior demonstrates that exponential damping of the tidal amplitude is only correct for a frictionless wave or an ideal estuary (no damping). However, in estuaries with modest damping (near ideal) it provides a reasonable approximation. In natural estuaries, there is generally a need to take account of local variability of, e.g., depth and friction, by subdividing the estuary into multiple reaches. This is illustrated with an example of the Scheldt estuary, which has been gradually deepened for navigation purpose over the last half century. The analytical model is used to study the effect of this deepening on the tidal dynamics in the main navigation channel, demonstrating that the navigation channel will become “overamplified” when it reaches a depth larger than the critical depth. In the case of overamplification, a further increase of the depth reduces the amplification until critical convergence (condition for a frictionless standing wave) is reached asymptotically. Finally, based on the ratio between the tidal amplitude at the seaward boundary and the asymptotic tidal amplitude, estuaries can be classified into damped, amplified, or ideal estuaries, which is illustrated with 23 real estuaries.

An analytical approach to determining resonance in semi-closed convergent tidal channels

An analytical model is used to investigate the resonant behavior in a semi-closed channel. The main integral quantities of the tidal wave are obtained by means of a linearized one-dimensional model as a function of three dimensionless parameters, representing cross-section convergence, friction and distance to the closed boundary. Arbitrary along-channel variations of width and depth are accounted for by using a multi-reach approach, whereby the main tidal dynamics are reconstructed by solving a set of linear equations satisfying the continuity conditions of water level and discharge at the junctions of the sub-reaches. We highlight the importance of depth variation in the momentum equation, which is not considered in the classical tidal theory. The model allows for a direct characterization of the resonant response and for the understanding of the relative importance of the controlling parameters, highlighting the role of convergence and friction. Subsequently, the analytical model is applied to the Bristol Channel and the Guadalquivir estuary. The proposed analytical relations provide direct insights into the tidal resonance in terms of tidal forcing, geometry and friction, which will be useful for the study of semi-closed tidal channels that experience relatively large tidal ranges at the closed end.

A coupled analytical model for salt intrusion and tides in convergent estuaries

ABSTRACT In this paper we develop a coupled analytical model for salinity and tidal propagation in estuaries where the cross-sectional area varies exponentially. A simple analytical model for tidal dynamics has been used to estimate the tidal excursion, which has an important influence on the salt intrusion process since it determines the extreme salinities (i.e. salinity distribution for high water slack and low water slack). The objective of the coupling is to reduce the number of calibration parameters, which subsequently strengthens the reliability of the salt intrusion model. Moreover, the coupling enables us to assess the potential impacts of external changes, both human-induced interventions (e.g. dredging) and natural changes (e.g. global sea level rise), on the salt intrusion process. In addition, the fully analytical solution for hydrodynamics allows immediate estimation of the tidally averaged depth and friction coefficient for given water level recordings and salinity measurements. This is particularly useful when a geometric survey is not available. The coupled model has been applied to six previously unsurveyed estuaries in Malaysia and the results show that the correspondence between analytical estimations and observations is very good. Thus, the coupled model proves to be a useful tool to obtain estimates of salt intrusion in estuaries based on a minimum amount of information required and for assessing the effect of human-induced or natural changes. EDITOR D. Koutsoyiannis ASSOCIATE EDITOR B. Dewals

Recent changes in the sediment regime of the Pearl River (South China): Causes and implications for the Pearl River Delta

1 Institute of Estuarine and Coastal Research, School of Marine Sciences, Sun Yat‐sen University, Guangzhou 510275, China State‐province Joint Engineering Laboratory of Estuarine Hydraulic Technology, Guangzhou 510275, China Guangdong Provincial Key Laboratory of Marine Resources and Coastal Engineering, Guangzhou 510275, China Correspondence Huayang Cai, Institute of Estuarine and Coastal Research, School of Marine Sciences, Sun Yat‐sen University, Guangzhou 510275, China. Email: caihy7@mail.sysu.edu.cn Funding information National Key Research and Development Program of China, Grant/Award Number: 2016YFC0402602; National Natural Science Foundation of China, Grant/Award Number: 41706088; Guangdong Provincal Natural Science Foundation of China, Grant/Award Number: 2017A030310435; Water Resource Science and Technology Innovation Program of Guangdong Province, Grant/Award Number: 2016‐21

Effects of Tidal-Forcing Variations on Tidal Properties Along a Narrow Convergent Estuary

A 1D analytical framework is implemented in a narrow convergent estuary that is 78 km in length (the Guadiana, Southern Iberia) to evaluate the tidal dynamics along the channel, including the effects of neap-spring amplitude variations at the mouth. The close match between the observations (damping from the mouth to ∼ 30 km, shoaling upstream) and outputs from semi-closed channel solutions indicates that the M2 tide is reflected at the estuary head. The model is used to determine the contribution of reflection to the dynamics of the propagating wave. This contribution is mainly confined to the upper one third of the estuary. The relatively constant mean wave height along the channel (< 10% variations) partly results from reflection effects that also modify significantly the wave celerity and the phase difference between tidal velocity and elevation (contradicting the definition of an “ideal” estuary). Furthermore, from the mouth to ∼ 50 km, the variable friction experienced by the incident wave at neap and spring tides produces wave shoaling and damping, respectively. As a result, the wave celerity is largest at neap tide along this lower reach, although the mean water level is highest in spring. Overall, the presented analytical framework is useful for describing the main tidal properties along estuaries considering various forcings (amplitude, period) at the estuary mouth and the proposed method could be applicable to other estuaries with small tidal amplitude to depth ratio and negligible river discharge.

Progressive change of tidal wave characteristics from the eastern Yellow Sea to the Asan Bay, a strongly convergent bay in the west coast of Korea

Although there have been studies on the tide in convergent bay (or estuary), the tide change in terms of phase speed, amplitude, and phase difference between elevation and tidal current from a coastal ocean to a convergent bay has not been clearly shown so far. This study systematically examines the change of tidal wave characteristics from the eastern Yellow Sea to the Asan Bay, a strongly convergent bay on the west coast of Korea, using observations and an analytical model. As the tidal wave propagates from the eastern Yellow Sea into the Asan Bay, the phase speed, amplitude, and phase difference between elevation and tidal current increase along the channel. Such a phenomenon represents a unique example of tide change from a coastal ocean to a convergent bay, indicating dominance of convergence over friction in the Asan Bay. Both analytically computed tidal amplitude and travelling time compare well with observations. In the Asan Bay, the influence of the reflected wave is only felt in the upper one fifth of the bay and is almost unperceivable in the rest of the bay. The analytical analyses presented in this paper are particularly useful for understanding the relative importance of channel convergence, bottom friction, and reflected wave on the tidal characteristics change along the channel and the proposed method could be applicable to other estuaries.

Impacts of estuarine mixing on vertical dispersion of polycyclic aromatic hydrocarbons (PAHs) in a tide-dominated estuary

To examine the impacts of estuarine mixing on the dispersion of polycyclic aromatic hydrocarbons (PAHs), seasonal variations in the vertical distribution of dissolved PAHs in the Humen River mouth of the Pearl River Estuary, which is a tide-dominated estuary, were thoroughly examined. An analysis of the vertical distribution of the concentration, composition and sources of PAHs indicates enhanced mixing of PAHs in January relative to June, which is strongly related to seasonal variations in the magnitude of estuarine mixing. Furthermore, the vertical distribution of PAHs initially indicated an increase and then a decrease from the surface layer to the bottom layer. In general, estuarine mixing promotes the vertical dispersion of PAHs, causing a more even PAHs distribution, while salinity stratification can trap PAHs, resulting in higher PAHs concentrations. Our study indicates that salinity variability stimulates significant dynamic effects regarding the dispersion of PAHs within estuarine environments.