A numerical study of horizontal dispersion in a macro tidal basin

Tidal circulation in Cobscook Bay, a macro tidal basin, is simulated using the three-dimensional, nonlinear, finite element ocean model, QUODDY_dry. Numerical particles are released from various transects in the bay at different tidal phases and tracked for several tidal cycles. Initially, nearby particles in the main tidal channel experience a great deal of spreading and straining, and after a few tidal cycles, they are separated in different parts of the bay. The fundamental mechanism for particle dispersion is the chaotic advection that arises from long tidal excursions passing through many residual eddies. A loosely correlated, inverse relationship between the two dimensionless parameters, ν (the ratio of the residual current to the tidal current) and λ (the ratio of the tidal excursion to the main topographic scale), can be constructed for large values of ν. Several Lagrangian statistical measures are used to quantify and distinguish dispersion regimes in different parts of Cobscook Bay. It is found that the effective Lagrangian dispersion coefficient can be estimated using the product of the magnitude of residual currents and the tidal excursion.     

Sand–mud morphodynamics in a short tidal basin

The influence of sand and mud transport on the morphological behaviour of a short tidal basin is investigated in this paper. For this purpose, a morphological model is applied in which sand and mud transport are included and the temporal and spatial bed composition variations are taken into account. Initially, the morphological development shows a sand wave near the entrance of the basin and a mud deposition wave more landward. A quasi equilibrium bed level profile is found after a long period (order century) with a sandy bed surface over almost the entire basin and only a small muddy area near the landward end. The dimensionless ratio between the deposition and erosion flux turns out to be a crucial parameter for the understanding of the observed behaviour. Comparison with previous studies on short tidal basins for sand indicates only that the presence of mud in a combined sand mud model does not change the equilibrium bed level profile considerably for the applied parameter settings herein, but drastically decreases the morphological time scale. Comparison between model results and field data of the Wadden Sea suggests that the obtained bed level and bed composition profile are realistic, indicating that the process-based sand mud model is a first step towards a better understanding of sand mud distributions in tidal basins.Responsible Editor: Jens Kappenberg     

A numerical study of island wake generated by an elliptical tidal flow

An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow.     

Flow fields and particle trajectories beneath a tidal bore: A numerical study

Tidal bores may appear in some estuaries when the tides quickly reach a high level. This phenomenon is rare but has a strong impact during its short duration: i.e. the river bed is significantly eroded and sediments are then transported. In this paper, the trajectories of suspended particles induced by this flow are numerically studied. Four undular bores with Froude numbers between 1.1 and 1.2 are studied. Despite similar Froude numbers, various initial flow conditions were selected to produce or not an inversion of the flow direction during the bore passage. The particle trajectories associated with each distinct flow configuration are presented and analyzed. These trajectories, estimated by solving the Maxey-Riley equation, appear to be very different even though the Froude numbers of flows are similar. These observations are important because the Froude number is often used to characterize a tidal bore as it describes well the free surface, however, it cannot describe the sediment transport. Finally, Chen's model of wave-current interactions is adapted to fit the cases studied and is applied to the four bores simulated. The results highlight that this latter model can reproduce the observed trajectories and dissociate their different components. From this model, it is shown that the inertial and Basset history effects can be neglected compared to the gravity and flow entrainment effects due to the viscous drag when one wants to determine the long-term trajectories of suspended particles.     

Modeling the tidal channel morphodynamics in a macro-tidal embayment,Hangzhou Bay,China

The Hangzhou Bay is a macro-tidal bay located to the south of the Changjiang estuary in China. Along its northern shore, a large-scale tidal channel system has developed, which includes a main northern tidal channel, with a length of more than 50 km and a width up to 10 km, and a secondary southern tidal channel. A process-based morphodynamic model, incorporating the cohesive sediment transport module of Delft3D, is used to analyze the physical processes and mechanisms underlying the formation and evolution of this tidal channel system. The results show that spatial gradients of flood dominance, caused by boundary enhancement via current convergences, is responsible for the formation of the channel system, due to a combination of the various factors such as funnel-shaped geometry hindering associated with the presence of islands, and flow deviation by the southern tidal flat and so on. The model results agree well with the real morphological features. This study also indicates that the reclamation of the southern tidal flat imposes a profound influence on the morphological evolution of the tidal channel system in the Hangzhou Bay. It is feasible to use the model to simulate long-term estuarine morphological changes with cohesive sediment settings.     

The role of salinity in fluvio-deltaic morphodynamics: A long-term modelling study

Salinity difference between terrestrial river discharge and oceanic tidal water plays a role in modifying the local flow field and, as a consequence, estuarine morphodynamics. Although widely recognized, recent numerical studies exploring the long-term morphological evolution of river-influenced estuaries with two-dimensional, depth-averaged models have mostly neglected salinity. Using a three-dimensional morphodynamic model, we aim to gain more insight into the effect of salinity on the morphodynamics of fluvio-deltaic systems. Model results indicate that the resultant estuarine morphology established after 600 years differs remarkably when a salinity gradient is included. A fan-shaped river-mouth delta exhibits less seaward expansion and is cut through by narrower channels when salinity is included. The inclusion of salinity tends to generate estuarine circulation, which favours landward sediment transport and hence limits the growth of the delta while enhancing the development of intertidal areas. The formation of deltaic channel–shoal patterns resulting from morphodynamic evolution tends to strengthen salinity stratification, which is characterized by an increased gradient Richardson number. The direction of the depth-averaged residual sediment transport over a tide may be opposite to the direction of residual velocity, indicating the significant influence of baroclinic effects on the net sediment transport direction (and hence morphological change). The effect of salinity on morphological evolution becomes less profound when the strength of tidal or fluvial forcing is dominant over the other. The effects of sediment type and flocculation, which are particularly important when salinity gradients are present, are also discussed. Overall, this study highlights that neglecting salinity to simulate long-term estuarine morphodynamics requires more careful justification, particularly when the environment is characterized by fine sediment types (favouring suspended transport), and relatively large river discharge and estuarine depth (favouring baroclinic effects). © 2020 John Wiley & Sons, Ltd.     

A depth-averaged tidal numerical model using non-orthogonal curvilinear co-ordinates

The two-dimensional shallow-water equations are developed for non-orthogonal curvilinear co-ordinates, in terms of the local deviations of the mesh from east and north. The equations are discretised and applied to a numerical model of tides in the Menai Strait in north Wales. The mesh is designed partially to fit the coastline and deep channels in the domain. After calibration, the model produces results which correspond well with measurements. This research was carried out while on sabbatical leave from University of Plymouth.     

Modeling equilibrium bed profiles of short tidal embayments

In many tidal embayments, bottom patterns, such as the channel-shoal systems of the Wadden Sea, are observed. To gain understanding of the mechanisms that result in these bottom patterns, an idealized model is developed and analyzed for short tidal embayments. In this model, the water motion is described by the depth- and width-averaged shallow water equations and forced by a prescribed sea surface elevation at the entrance of the embayment. The bed evolves due to the divergence and convergence of suspended sediment fluxes. To model this suspended-load sediment transport, the three-dimensional advection–diffusion equation is integrated over depth and averaged over the width. One of the sediment fluxes in the resulting one-dimensional advection–diffusion equation is proportional to the gradient of the local water depth. In most models, this topographically induced flux is not present. Using standard continuation techniques, morphodynamic equilibria are obtained for different parameter values and forcing conditions. The bathymetry of the resulting equilibrium bed profiles and their dependency on parameters, such as the phase difference between the externally prescribed M₂ and M₄ tide and the sediment fall velocity, are explained physically. With this model, it is then shown that for embayments that are dominated by a net import of sediment, morphodynamic equilibria only exist up to a maximum embayment length. Furthermore, the sensitivity of the model to different morphological boundary conditions at the entrance of the embayment is investigated and it is demonstrated how this strongly influences the shape and number of possible equilibrium bottom profiles. This paper ends with a comparison between the developed model and field data for the Wadden Sea’s Ameland and Frisian inlets. When the model is forced with the observed M₂ and M₄ tidal constituents, morphodynamic equilibria can be found with embayment lengths similar to those observed in these inlets. However, this is only possible when the topographically induced suspended sediment flux is included. Without this flux, the maximum embayment length for which morphodynamic equilibria can be found is approximately a third of the observed length. The sensitivity of the model to the topographically induced sediment flux is discussed in detail.     

Observation and numerical modeling of tidal dune dynamics

Tidal sand dune dynamics is observed for two tidal cycles in the Arcachon tidal inlet, southwest France. An array of instruments is deployed to measure bathymetric and current variations along dune profiles. Based on the measurements, dune crest horizontal and vertical displacements are quantified and show important dynamics in phase with tidal currents. We observed superimposed ripples on the dune stoss side and front, migrating and changing polarity as tidal currents reverse. A 2D RANS numerical model is used to simulate the morphodynamic evolution of a flat non-cohesive sand bed submitted to a tidal current. The model reproduces the bed evolution until a field of sand bedforms is obtained that are comparable with observed superimposed ripples in terms of geometrical dimensions and dynamics. The model is then applied to simulate the dynamics of a field of large sand dunes of similar size as the dunes observed in situ. In both cases, simulation results compare well with measurements qualitatively and quantitatively. This research allows for a better understanding of tidal sand dune and superimposed ripple morphodynamics and opens new perspectives for the use of numerical models to predict their evolution.     

A test of equilibrium theory and a demonstration of its practical application for predicting the morphodynamics of the Yangtze River

Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial‐channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self‐adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer‐Peter and Müller bedload relation and relations of flow continuity and resistance we show that the Meyer‐Peter and Müller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright © 2014 John Wiley & Sons, Ltd.     

A numerical study of damping

Diagonal damping matrices were computed for three systems which have non-proportional damping matrices. These diagonal damping matrices were computed on three bases, as follows: 1. After normalizing the equations of motion by the modal matrix, the diagonal terms are retained ignoring the non-diagonal terms. 2. Diagonal damping matrix is established by the optimization algorithm which minimizes the mean square error of the frequency response. 3. Diagonal damping is determined from the normalized differential equation by matching the peaks of the coupled and uncoupled system. The frequency responses for the three cases of one of the three systems are presented together with a comparison of the energy dissipation.     

A numerical study of contrail development

In this study, the formation of a contrail from an aircraft flying near the tropopause is simulated using a three-dimensional mesoscale atmospheric model including a very complex scheme of parameterized cloud microphysical processes. Two different primary ice nucleation parameterizations for deposition nucleation, condensation freezing, and contact freezing are applied. The model-predicted ice concentrations are compared to data measured during the International Cirrus Experiment (ICE), 1989.     

The impacts of the large-scale hydraulic structures on tidal dynamics in open-type bay: numerical study in Jakarta Bay

The construction of a Giant Sea Wall (GSW) complex in Jakarta Bay has been proposed to protect Jakarta against flood in the Master Plan for National Capital Integrated Coastal Development (NCICD). However, these large-scale hydraulic structures could significantly change the tidal dynamics in Jakarta Bay. This research investigates the potential impacts of a GSW on the tidal dynamics, including tides, currents, and residual currents in Jakarta Bay using a validated numerical model (Finite Volume Coastal Ocean Model (FVCOM)). Results show that the bay is diurnal with a maximum tidal range of ~0.9 m. The flow is mainly in an east-west direction with a maximum depth-mean current speed of up to 0.3 ms^?1. The construction of a GSW would modulate the tidal dynamics by changing the bathymetry, tidal prism, wind effect, and tidal choking effect in the bay. The maximum tidal range would be slightly increased due to the reduced tidal prism of the bay and the increased tidal choking effect. The current would penetrate into the west reservoir through the gates and channels between the artificial islands, with peak speed jets appearing at the gates (~0.3 ms^?1), due to tidal choking. A similar peak current speed appears near the right wing of the GSW due to the pressure gradient would be created by the wing of the GSW. Closing the gates would mainly affect the currents inside the west reservoir. The residual current would be slightly increased after the construction of the GSW. An eddy would be formed at the bottom level near the right wing of the GSW. The direction of the residual current is landward instead of seaward at the surface level outside the GSW. The impact of wind on surface currents would be much reduced due to the decreased water surface area. Although this study is site specific, the findings may have a wider applicability to the impacts of large-scale hydraulic structures on tidal dynamics in open-type bays.     

A numerical study of the barotropic tides and tidal energy distribution in the Indonesian seas with the assimilated finite volume coastal ocean model

The tides and tidal energetics in the Indonesian seas are simulated using a three-dimensional finite volume coastal ocean model. The high-resolution coastline-fitted model is configured to better resolve the hydrodynamic processes around the numerous barrier islands. A large model domain is adopted to minimize the uncertainty adjacent to open boundaries. The model results with elevation assimilation based on a simple nudge scheme faithfully reproduced the general features of the barotropic tides in the Indonesian Seas. The mean root-mean-square errors between the observed and simulated tidal constants are 2.3, 1.1, 2.4, and 1.5 cm for M₂, S₂, K₁, and O₁, respectively. Analysis of the model solutions indicates that the semidiurnal tides in the Indonesian Seas are primarily dominated by the Indian Ocean, whereas the diurnal tides in this region are mainly influenced by the Pacific Ocean, which is consistent with previous studies. Examinations of tidal energy transport reveal that the tidal energy for both of the simulated tidal constituents are transported from the Indian Ocean into the IS mainly through the Lombok Strait and the Timor Sea, whereas only M₂ energy enters the Banda Sea and continues northward. The tidal energy dissipates the most in the passages on both sides of Timor Island, with the maximum M₂ and K₁ tidal energy transport reaching about 750 and 650 kW m^–1, respectively. The total energy losses of the four dominant constituents in the IS are nearly 338 GW, with the M₂ constituent dissipating 240.8 GW. It is also shown that the bottom dissipation rate for the M₂ tide is about 1–2 order of magnitudes larger than that of the other three tidal components in the Indonesian seas.     

Experimental analysis of tidal network growth and development

In this paper we present the results of a first series of laboratory experiments carried out in a large experimental apparatus, aimed at reproducing a typical lagoonal environment subject to tidal forcings. The experiments were designed in order to improve our understanding of the main processes governing tidal network initiation and its progressive morphodynamic evolution. During the experiments we observed the growth and development of tidal networks and analyzed their most relevant geomorphic features, taking into account the role played by the characteristics of the tidal forcing in driving the development of channeled patterns. The synthetic networks displayed geomorphic features which compare favorably with those of actual networks, showing that our experimental framework proves useful for analyzing the processes governing the formation and evolution of tidal channel networks. In particular, the synthetic networks develop via headward growth driven by the exceedance of a critical bottom shear stress, and display width-to-depth ratios and seaward exponential widening in accordance with observational evidence. Furthermore experimental networks reproduce statistical network characteristics of geomorphic relevance, such as the exponential probability distribution of unchanneled path lengths.     

Benchmark on the numerical simulations of the hydrodynamic and morphodynamic evolution of tidal channels and tidal inlets

A correct understanding of the hydrodynamics and morphodynamics of tidal basins is of fundamental importance for the fate of the Venice Lagoon, Italy. If on one hand, the development of sophisticated numerical models is called for in order to reproduce the complexity of the mechanisms governing the morphodynamic evolution of many natural environments, including lagoons, on the other hand, a clear knowledge of the reliability and limits of the results provided by these models is crucial in order to establish the condition under which they can be safely applied. To this aim, researchers involved in numerical modeling in the framework of the recent Corila research programmes, agreed to perform an accurate comparison of results provided by three different numerical models, applying them to the test case offered by the experimental investigations performed under controlled conditions by Tambroni et al. (2005a). Here, we consider the following numerical models: (i) a 2D finite element hydrodynamic model coupled with a 2D finite volume morphodynamic model (5 and 3); (ii) a 2D finite element morphodynamic model (Ferrarin et al., 2008); (iii) a 2D depth-averaged model for the inlet region, coupled with a 1D model for the channel (Tambroni et al., 2005b). A first set of simulations concerns the fixed bed case and shows that all the models provide similar results: in particular, they are able to predict the observed free surface oscillations satisfactorily, while comparison with the measured velocity field is less satisfactory. Moreover, as far as the flow field at the inlet is concerned, the models describe accurately the potential flow into the channel during the flood phase, while they are not able to adequately reproduce the occurrence of the fine structure of the shear layers shed by the inlet edges during the ebb phase. This limit is related to the shallow water character of the models. As for the morphodynamics, the long term equilibrium configurations of the bottom of the channel and of the near inlet region show qualitative agreement with the experimental observations, although in this case the differences between the results provided by the distinct numerical approaches are more marked.     

基于强震台网的我国沿海海啸走时预警

经济快速发展的中国沿海地区,面临着潜在海啸袭击危险。海啸传播走时分析是海啸预警系统的重要组成部分。本文基于强震台网提供的地震要素,从理论上讨论海啸预警时间计算方法。在球坐标系下,建立了远洋海啸传播模型,采用差分技术,实现远洋海啸传播数值模拟,首次针对我国主要城市进行了海啸走时计算,分析了我国沿海走时特点,指出了未来发生在太平洋的远洋海啸对我国的长江三角洲会有较大影响。本文计算海啸走时方法可以为我国建设的新一代基于数值海啸预警系统提供技术支持。     

A depth-dependent study of the topographic rectification of tidal currents

Abstract

A depth-dependent model for the topographic rectification of tidal currents in a homogeneous rotating fluid is used to examine the dependence of the rectified mean flow on various tidal, topographic and frictional parameters. Friction is parameterized through a vertically-uniform, time-independent vertical eddy viscosity and a bottom stress law applied near the top of the constant stress layer. The model neglects the interaction of mean and tidal currents, assumes uniformity along isobaths, and is closed with the assumption of zero depth-averaged mean flow across isobaths.

In the limit of depth-independence, the model reduces to that considered by Huthnance (1973) and Loder (1980) which, for weak friction, favours anticyclonic mean circulation around shallow regions and Lagrangian flow which is significantly reduced from the Eulerian. With the inclusion of vertical structure, the magnitude of the anticyclonic flow is amplified suggesting that depth-independent models may underestimate the along-isobath flow. For strong friction the direction of the mean flow depends on the orientation of the tidal ellipse relative to the isobaths. The depthindependent model again underestimates the magnitude of the along-isobath flow, but this can be offset with an appropriate reduction of the bottom friction coefficient.

The cross-isobath mean flows are one to two orders of magnitude weaker than the along-isobath flows and generally have more vertical structure. There is also a significant Stokes drift in the cross-isobath direction. Although there is some tendency for the cross-isobath mean bottom current to be down the cross-isobath mean pressure gradient, it appears that it is not generally possible to infer this current from depth-independent models.     

Multiple equilibrium states of the Gulf of Mexico Loop Current

It has been established that idealized western boundary currents, which encounter a gap in their supporting boundary, will assume one of two dominant steady states: a loop current state and a gap leaping state, and that transitions between these states display hysteresis. However, a question of whether the idealized geometries considered to date apply to the Gulf of Mexico Loop Current (LC) remained. Here, the nonlinear potential vorticity advection-diffusions equations are solved, for Gulf of Mexico topography, using Newton’s method. We demonstrate that, in application to the LC in the Gulf of Mexico, the original conclusions do hold and additionally describe peculiarities of the more realistic steady states. The existence of our numerically calculated steady LC states in the actual Gulf of Mexico are supported through analysis of historical sea surface height data, and implications of our results for LC modeling and forecasting are discussed.

     

Two-dimensional equilibrium morphological modelling of a tidal inlet: an entropy based approach

The management of tidal inlets requires the accurate prediction of equilibrium morphologies. In areas where the flow from rivers is highly regulated, it is important to give decision makers the ability to determine optimal flow management schemes, in order to allow tidal inlets to function as naturally as possible, and minimise the risk of inlet closure. The River Murray Mouth in South Australia is one such problem area. Drought and the retention of water for irrigation and urban water consumption have limited the amount of water entering the estuary. As a result, sediment from the coastal environment is being deposited in the mouth of the estuary, reducing the effect of further coastal interactions. Currently, situations such as this are modelled using traditional process-based methods, where wave, current, sediment transport and sediment balance modules are linked together in a time-stepping process. The modules are reapplied and assessed until a stable morphology is formed. In this paper, new options for modelling equilibrium morphologies of tidal inlets are detailed, which alleviate some of the shortfalls of traditional process-based models, such as the amplification of small errors and reliance on initial conditions. The modelling problem is approached in this paper from a different angle and involves the use of entropy based objective functions, which are optimised in order to find equilibrium morphologies. In this way, characteristics of a system at equilibrium can be recognised and a stable system predicted without having to step through time. This paper also details the use of self-organisation based modelling methods, another non-traditional model application, where local laws and feedback result in the formation of a global stable equilibrium morphology. These methods represent a different approach to traditional models, without some of the characteristics that may add to their limitations. Responsible Editor: Alejandro Souza