On the stability relationships between tidal asymmetry and morphologies of tidal basins and estuaries

Simple stability relationships are practically useful to provide a rapid assessment of coastal and estuarine landforms in response to human interventions and long‐term climate change. In this contribution, we review a variety of simple stability relationships which are based on the analysis of tidal asymmetry (TA). Most of the existing TA‐based stability relationships are derived using the one‐dimensional tidal flow equations assuming a certain regular shape of the tidal channel cross‐sections. To facilitate analytical solutions, specific assumptions inevitably need to be made, for example by linearizing the friction term and dropping some negligible terms in the tidal flow equations. We find that three major types of TA‐based stability relationships have been proposed between three non‐dimensional channel geometric ratios (represented by the ratio of channel widths, ratio of wet surface areas and ratio of storage volumes) and the tide‐related parameter a/h (i.e. the ratio between tidal amplitude and mean water depth). Based on established geometric relations, we use these non‐dimensional ratios to restate the existing relationships so that they are directly comparable. Available datasets are further extended to examine the utility of these TA‐based relationships. Although a certain agreement is shown for these relationships, we also observe a large scatter of data points which are collected in different types of landscape, hydrodynamic and sedimentological settings over the world. We discuss in detail the potential reasons for this large scatter and subsequently elaborate on the limited applicability of the various TA‐based stability relationships for practical use. We highlight the need to delve further into what constitutes equilibrium and what is needed to develop more robust measures to determine the morphological state of these systems. Copyright © 2018 John Wiley & Sons, Ltd.     

Transverse structure of tidal and residual flow and sediment concentration in estuaries

An analytical and a numerical model are used to understand the response of velocity and sediment distributions over Gaussian-shaped estuarine cross-sections to changes in tidal forcing and water depth. The estuaries considered here are characterized by strong mixing and a relatively weak along-channel density gradient. It is also examined under what conditions the fast, two-dimensional analytical flow model yields results that agree with those obtained with the more complex three-dimensional numerical model. The analytical model reproduces and explains the main velocity and sediment characteristics in large parts of the parameter space considered (average tidal velocity amplitude, 0.1–1 m s^− 1 and maximum water depth, 10–60 m). Its skills are lower for along-channel residual flows if nonlinearities are moderate to high (strong tides in deep estuaries) and for transverse flows and residual sediment concentrations if the Ekman number is small (weak tides in deep estuaries). An important new aspect of the analytical model is the incorporation of tidal variations in the across-channel density gradient, causing a double circulation pattern in the transverse flow during slack tides. The gradient also leads to a new tidally rectified residual flow component via net advection of along-channel tidal momentum by the density-induced transverse tidal flow. The component features landward currents in the channel and seaward currents over the slopes and is particularly effective in deeper water. It acts jointly with components induced by horizontal density differences, Coriolis-induced tidal rectification and Stokes discharge, resulting in different along-channel residual flow regimes. The residual across-channel density gradient is crucial for the residual transverse circulation and for the residual sediment concentration. The clockwise density-induced circulation traps sediment in the fresher water over the left slope (looking up-estuary in the northern hemisphere). Model results are largely consistent with available field data of well-mixed estuaries.     

地中海涡旋的垂向结构与物理性质

本文利用地震海洋学新的反演结果,对地中海涡旋的温度、密度、声速以及波阻抗等物理性质进行了详细的分析与讨论,特别对地中海涡旋的一些细结构、混合过程进行了相关描述.研究分析取得以下认识:(1)涡旋具有涡旋核心水与涡旋混合水双层结构,这种结构特征可以在温度图、声速图和波阻抗图中识别出来;(2)涡旋核心水并不是均匀的稳定结构,内部有微弱的混合作用;(3)在涡旋上部以及周围边缘区域,海水的混合比较复杂;在涡旋下部边缘区域,除了有小尺度的盐指混合,内波也是非常重要的动力混合作用;(4)海水密度在涡旋核心水的分布比较稳定,成层性较强,在混合水区域由于不同的混合作用及其强烈程度不同,会发生波动甚至反转;(5)涡旋本身并不是一个严格对称的结构,涡旋与背景海水的上部以及周围边界比较模糊和复杂,而涡旋下部边界则比较明显.地震海洋学反演提供的涡旋物理性质数据能够为涡旋进一步的研究提供更为准确、更高精度以及更高分辨率的参考数据,同时对涡旋的运动学以及动力学研究提供了更进一步的研究方法和研究方向.     

A three-dimensional numerical sea model with eddy viscosity varying piecewise linearly in the vertical

The solution of the three-dimensional linear hydrodynamic equations which describe wind-driven flow in a homogeneous sea are solved using the eigenfunction method. The eddy viscosity is taken to vary piecewise linearly in the vertical over an arbitrary number of layers. Using this formulation the eigenfunctions are given in terms of Bessel functions. The coefficients of integration as well as the eigenvalues are determined accurately such that the boundary conditions are satisfied. Values of the eigenfunctions at any depth can then be determined very fast and to a high degree of accuracy.Current profiles at any position can hence be computed accurately. The expansion of the horizontal component of current converges very fast at all depths.     

The vertical structure of tidal currents and other oscillatory flows

Assuming a linearized equation of motion in the absence of stratification, the vertical structure of tidal currents is shown to be a function of two dimensionless parameters. The first of these, Y = (ω/E)1/2D, is analogous to an Ekman height with ω the tidal frequency, D the depth, and E the (constant) vertical eddy viscosity. The second parameter, J = (ωE)1/2[(8/3π)kŪ], introduces the effect of a quadratic bed stress through the bed-stress coefficient k and the depth-averaged velocityÜ. From these it is possible to illustrate the full range of possible vertical structure and to understand the basic scaling laws involved.By assuming E =aU¯D good agreement between theory and observation was found. With this assumption vertical structure reduces to a function of just one parameter, namely kS, where S =Ū2π/Dω is the Strouhal number.By resolving tidal current ellipses into clockwise and anticlockwise rotating components the original theory developed for recti-linear flow can be applied to fully three-dimensional flow. In this way, many of the observed characteristics of current structure in shallow seas may be explained.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.     

The relationship between vertical eddy diffusion and buoyancy gradient in the deep sea

Vertical eddy diffusivities (K_v's) have been estimated at fourteen widely separated locations from fourteen²²²Rn profiles and two²²⁸Ra profiles measured near the ocean floor as part of the Atlantic and Pacific GEOSECS programs. They show an inverse proportionality to the local buoyancy gradient [(g/?)(??_pot/?z)] calculated from hydrographic measurements. The negative of the constant of proportionality is the buoyancy flux [?K_v(g/?)(??_pot/?z)] which has a mean of ?4 × 10^?6 cm²/sec³. Our results suggest that the buoyancy flux varies very little near the ocean floor. K_v's for the interior of the deep Pacific calculated from the relationship K_v = (4 × 10^?6cm²/sec³)/[(g/?)(??_pot/?z)] agree well with published estimates. K_v's calculated for the pycnocline are one to two orders of magnitude smaller than upper limits estimated from tritium and⁷Be distributions.Heat fluxes calculated with the model K_v's obtained from the²²²Rn profiles average 31 μcal cm^?2 sec^?1 in the Atlantic Ocean and 8 μcal cm^?2 sec^?1 in the Pacific Ocean.     

The effect of tidal asymmetry and temporal settling lag on sediment trapping in tidal estuaries

Over decades and centuries, the mean depth of estuaries changes due to sea-level rise, land subsidence, infilling, and dredging projects. These processes produce changes in relative roughness (friction) and mixing, resulting in fundamental changes in the characteristics of the horizontal (velocity) and vertical tides (sea surface elevation) and the dynamics of sediment trapping. To investigate such changes, a 2DV model is developed. The model equations consist of the width-averaged shallow water equations and a sediment balance equation. Together with the condition of morphodynamic equilibrium, these equations are solved analytically by making a regular expansion of the various physical variables in a small parameter. Using these analytic solutions, we are able to gain insight into the fundamental physical processes resulting in sediment trapping in an estuary by studying various forcings separately. As a case study, we consider the Ems estuary. Between 1980 and 2005, successive deepening of the Ems estuary has significantly altered the tidal and sediment dynamics. The tidal range and the surface sediment concentration has increased and the position of the turbidity zone has shifted into the freshwater zone. The model is used to determine the causes of these historical changes. It is found that the increase of the tidal amplitude toward the end of the embayment is the combined effect of the deepening of the estuary and a 37% and 50% reduction in the vertical eddy viscosity and stress parameter, respectively. The physical mechanism resulting in the trapping of sediment, the number of trapping regions, and their sensitivity to grain size are explained by careful analysis of the various contributions of the residual sediment transport. It is found that sediment is trapped in the estuary by a delicate balance between the M ₂ transport and the residual transport for fine sediment ( $\emph{w}_s=0.2$  mm s^???1) and the residual, M ₂ and M ₄ transports for coarser sediment ( $\emph{w}_s=2$  mm s^???1). The upstream movement of the estuarine turbidity maximum into the freshwater zone in 2005 is mainly the result of changes in tidal asymmetry. Moreover, the difference between the sediment distribution for different grain sizes in the same year can be attributed to changes in the temporal settling lag.     

Vertical structure of tidal current in a typically coastal raft-culture area

In this paper vertical structure of tidal current in a typically coastal raft-culture area is discussed by field measurement and a numerical model. The observations show that the vertical structure changed dramatically. A tidal surface boundary layer (SBL) is well formed due to the frictional effects induced by extensive, high-density suspended culture as surface obstruction. Both the aquaculture drag and the bottom friction are much higher than those in non-raft-culture areas, and show an obvious variation with tidal flow. The significant earlier ebbing and earlier flooding appear in the upper water column instead of the seabed. And the maximal phase lag is about 1 h within one tide cycle. A 1D hydrodynamic model was modified to include the SBL and parameterized with the field data. It replicated the observed velocity profile and was then used to investigate the impacts of varying culture density and bottom friction on the vertical tidal-current structure. Modeling results indicate that the surface current velocity was largely damped because culture activities enhanced the frictional effects on flow intensively. The magnitude and vertical structure of tidal current are determined together with aquaculture drag and bottom friction. In addition, the vertical velocity structure has a nonlinear trend along with culture density and bottom friction. This study is a theoretical foundation for optimizing aquaculture configuration through regulating culture density and species distribution.     

Wave direction shift triggered severe erosion of beaches in estuaries and bays with limited post-storm recovery

Many estuaries contain sandy beaches that provide habitats and offer protective buffers for wetlands and infrastructure, alongside cultural and recreational resources. Research underpinning coastal management tends to focus on tide- and swell-dominated sandy beaches, but little attention is given to beaches in estuaries and bays (BEBs) that exist along a continuum of wind/swell wave, tide and riverine influence. BEBs are subject to less wave energy than open coast locations because of the generally narrow window of directions for which ocean waves can propagate through the entrance. However, when storm wave direction coincides with the orientation of the estuary or bay entrance, waves can penetrate several kilometres inside. Here we focus on eight BEBs in two major bays/estuaries in Sydney, Australia and present observations from before and after a major extratropical storm with waves from an atypical direction in June 2016. We quantify magnitudes of beach erosion and recovery rates for 3 years post-storm. We show that when high-energy storm waves penetrate bays and estuaries, BEBs can undergo up to 100% of subaerial beach erosion. Three years after the storm, only 5 of the 29 (17%) eroded subaerial beach profiles had recovered to their pre-storm volume. This is likely due to the lack of low-frequency, beach-building waves at BEBs under modal weather conditions in between storms, in contrast to open coast beaches. We also show that the recovery of BEBs may be limited by the absence of adjacent sediment reservoirs due to the dominance of tidal processes mid-channel. Our study highlights the unique behaviour of BEBs relative to beaches on the open coast, and that shifting wave direction needs to be considered in long-term beach resilience under climate change. © 2020 John Wiley & Sons, Ltd.     

Analytical and numerical analysis of tides and salinities in estuaries; part I: tidal wave propagation in convergent estuaries

Analytical solutions of the momentum and energy equations for tidal flow are studied. Analytical solutions are well known for prismatic channels but are less well known for converging channels. As most estuaries have a planform with converging channels, the attention in this paper is fully focused on converging tidal channels. It will be shown that the tidal range along converging channels can be described by relatively simple expressions solving the energy and momentum equations (new approaches). The semi-analytical solution of the energy equation includes quadratic (nonlinear) bottom friction. The analytical solution of the continuity and momentum equations is only possible for linearized bottom friction. The linearized analytical solution is presented for sinusoidal tidal waves with and without reflection in strongly convergent (funnel type) channels. Using these approaches, simple and powerful tools (spreadsheet models) for tidal analysis of amplified and damped tidal wave propagation in converging estuaries have been developed. The analytical solutions are compared with the results of numerical solutions and with measured data of the Western Scheldt Estuary in the Netherlands, the Hooghly Estuary in India and the Delaware Estuary in the USA. The analytical solutions show surprisingly good agreement with measured tidal ranges in these large-scale tidal systems. Convergence is found to be dominant in long and deep-converging channels resulting in an amplified tidal range, whereas bottom friction is generally dominant in shallow converging channels resulting in a damped tidal range. Reflection in closed-end channels is important in the most landward 1/3 length of the total channel length. In strongly convergent channels with a single forward propagating tidal wave, there is a phase lead of the horizontal and vertical tide close to 90^o, mimicking a standing wave system (apparent standing wave).     

Morphological and sedimentary features of sandy-muddy transitional beaches in estuaries and bays along mesotidal to macrotidal coasts

Sandy-muddy transitional beaches (SMT-Beaches), representing the transition from sandy beaches to tidal mudflats, should theoretically develop very different morphological and sedimentological characteristics in river estuaries and in semi-enclosed bays due to their contrasting dynamic sedimentary environments. Evidence, however, is rare in the scientific literature. To reveal these morphological and sedimentary differences, the sand–mud transition (SMT) boundary distribution, beach profiles, and surface and downcore sediment grain-size compositions of 27 SMT-Beaches located along mesotidal to macrotidal coasts of the western Taiwan Strait, southeastern China, were investigated. The results show that typical estuarine SMT-Beaches are mainly characterized by an ambiguous SMT, a long distance between the SMT and the coastline (31–302 m), lower SMT and inflection point altitudes (average –0.76 m and –0.04 m), and lower upper beach gradients (~0.068) with fine sand. Estuarine SMT-Beach sediments display clear interbedded mud and sand layers, implying potential SMT migrations over various timescales. By contrast, typical bay SMT-Beaches are characterized by distinct SMT, a short distance between the SMT and the coastline (11–52 m), higher SMT and inflection point altitudes (~0.24 m and ~0.35 m), and narrower upper beaches with higher gradients (~0.095) and coarse sand. Bay SMT-Beaches present relatively stable sedimentary sequences and a narrow gravel belt surrounding the inflection point and/or SMT. These morphological and sedimentary differences between the two SMT-Beach types are initially constrained by sediment supply and transport and are further affected by tide conditions and wave climate. Sediment supply and transport predominately control the sediment structures, while the tidal range strongly influences spatial variations in SMT distances. Wave climate normally drives SMT altitude variations. This study highlights the morphological and sedimentary differences in SMT-Beaches in estuaries and bays, providing important knowledge for further revealing their morphodynamic processes and potential future nourishment. © 2020 John Wiley & Sons, Ltd.     

Analytical study of the transverse distribution of along-channel and transverse residual flows in tidal estuaries

We present an analytical model to decompose complex along-channel and transverse residual flows into components induced by individual mechanisms. The model describes the transverse distribution of residual flows in tidally dominated estuaries. Scaling and perturbation techniques are used to obtain analytical solutions for residual flows over arbitrary across-channel bed profiles. The flows are induced by horizontal density gradients, tidal rectification processes, river discharge, wind, channel curvature and the earth's rotation. These rectification processes induce residual flows that are up-estuary to the right and down-estuary to the left of an estuarine channel (looking up-estuary in the northern hemisphere). The tidal rectification processes fundamentally change the transverse structure of along-channel residual flows in many tidal estuaries, as these processes cause the flows to be internally asymmetric about the mid-axis of the channel for relatively large tidal velocities, steep channels or narrow estuaries. In addition, velocity scales are derived from the analytical solutions to estimate the relative importance of the various residual flow mechanisms from estuarine parameters. A case study of a transect across the Upper Chesapeake Bay showed that important features of the residual flow observed in that transect are reproduced and explained by the analytical model. The velocity scales were able to identify the relevant residual flow mechanisms as well. The tidal rectification processes considered here result from advection of along-channel tidal momentum by Coriolis-induced transverse tidal currents.     

Analytical solution to the 3D tide-induced Lagrangian residual current in a narrow bay with vertically varying eddy viscosity coefficient

Ocean Dynamics - The 3D Lagrangian residual velocity (LRV) is solved analytically in a narrow bay employing a vertically varying eddy viscosity coefficient. The nondimensional vertical profile of...     

Coupling of one- and two-dimensional finite elements for the computation of tidal flow in estuaries

A new method for the numerical computation of tidal flow in estuaries is demonstrated. One- and two-dimensional finite elements are directly coupled in a single model requiring the solution of only one common set of equations for all unknown parameters in each time step. The utility of the method is demonstrated with the computation of the tide in the Elbe Estuary. The computed water levels are compared with measured hydrographs at different gauges on the Elbe River.     

Celtic Sea and Armorican current structure and the vertical distributions of temperature and chlorophyll

Vertical sections of temperature and chlorophyll a across the slopes and shelf of the Celtic Sea in the summer show the characteristic regimes; oceanic, slope, shelf, frontal, and mixed. Increases of surface chlorophyll a are commonly observed along the shelf tidal fronts where the thermocline outcrops at the surface, and also at the shelf-break. The variations in phytoplankton biomass are most readily interpreted in terms of the effects of physical mixing processes due to wind and tide on the availability of inorganic nutrients and light energy. On the shelf, mixing processes, both due to internal waves, inertial currents, and to boundary induced turbulence caused by tidal shear associated with the sea floor, play an important role in determining the observed vertical structures. A numerical model is used to define regions where tidal mixing processes are likely to be relatively important and provides the physical framework for interpreting the temperature and chlorophyll a profiles.     

Importance of cross-channel bathymetry and eddy viscosity parameterisation in modelling estuarine flow

For a proper understanding of flow patterns in curved tidal channels, quantification of contributions from individual physical mechanisms is essential. We study quantitatively how such contributions are affected by cross-channel bathymetry and three alternative eddy viscosity parameterisations. Two models are presented for this purpose, both describing flow in curved but otherwise prismatic channels with an (almost) arbitrary transverse bathymetry. One is a numerical model based on the full three-dimensional shallow water equations. Special feature of this diagnostic model is that assumptions regarding the relative importance of particular physical mechanisms can be incorporated in the computations by switching corresponding terms in the model equations on or off. We also present an idealized model that provides semi-analytical approximate solutions of the shallow water equations for all three considered alternative eddy viscosity parameterisations. It forms an aid in explaining and theorising about results obtained with the numerical model. Observations regarding Chesapeake Bay serve as a reference case for the present study. We find that the relative importance of both along-channel advective forcing and transverse diffusive forcing depends on local characteristics of the cross-sectional bottom profile rather than global ones. In our reference case, tide-residual along-channel flow induced by these forcings is not small compared to the total tidal residual. Building on this observation, we present an indicative test to judge whether advective processes should be included in leading order in modelling tide-dominated estuarine flow. Furthermore, depending on the applied eddy viscosity parameterisation (uniformly or parabolically distributed over the vertical), we find qualitatively different spatial patterns for the along-channel advective forcing.