Modeling profile shape evolution for accreting tidal flats composed of mud and sand: A case study of the central Jiangsu coast, China

The evolution of the shore-normal profile shape of accreting tidal flats is controlled mainly by tidally induced mud and sand transport. To understand the evolution processes, a model is developed to simulate the tidal flat profile changes in response to spring-neap tidal cycles. The model treats both sand and mud transport patterns over the tidal flats and adopts an algorithm to deal with the areas near the high water (HW) level on springs. The model is applied to an accreting tidal flat on the central Jiangsu coast, to investigate the relationship between the equilibrium profile shape of the tidal flat and the various influencing factors (e.g. initial profile shape of tidal flat, tidal range and sediment supply). Based on the modeling results the following conclusions are derived: (1) the accreting tidal flat tends to be convex in profile shape when it reaches an equilibrium state; (2) sediment supply is a key factor affecting the width and accretion-erosion status of the tidal flat; (3) filling the area close to high water (HW) on spring tides is essential for reproducing the shape evolution and the morphodynamic behavior of tidal flats; (4) after an equilibrium shape is formed, a tidal flat with abundant sediment supply can steadily prograde to seaward, at the same time maintaining the equilibrium shape; and (5) the modeled width and the slope of the tidal flat are consistent with those of the central Jiangsu coast when the parameters adopted in the model are appropriate for the local conditions.     

Effect of channel deepening on tidal flow and sediment transport—part II: muddy channels

Natural tidal channels often need deepening for navigation purposes (larger vessels). The depth increase may lead to tidal amplification, salt intrusion over longer distances, and increasing sand and mud import. Increasing fine sediment import, in turn, may start a process in which the sediment concentration progressively increases until the river becomes hyper-turbid, which may lead to increased dredging volumes and to decreased ecological values. These effects can be modeled and studied using detailed 3D models. Reliable simplified models for a first quick engineering evaluation are however lacking. In this paper, we apply both simplified and detailed 3D models to analyze the effects of channel deepening in prismatic and weakly converging tidal channels with saturated mud flow. The objective is to gain quantitative understanding of the effects of channel deepening on mud transport. We developed a simplified tidal mud model describing most relevant processes and effects in saturated mud flows with only minor horizontal transport gradients (quasi uniform conditions). The simplified model is not valid for non-saturated mud flow conditions. This model can either be used in standalone mode or in post-processing mode with computed near-bed velocities from a 3D hydrodynamic model as an input. The standalone model has been compared to various field data sets. Mud transport processes in the mouth region of muddy tidal channels can be realistically represented by the simplified model, if sufficient salinity and sediment data are available for calibration. The simulation of tidal mud transport and the behavior of an estuarine turbidity maximum (ETM) in saturated and non-saturated mud flow conditions cannot be represented by the simplified model and requires the application of a detailed 3D model.     

中国东西重力潮汐剖面

为了检验体潮与海潮的理论模型,分析了中国东西重力潮汐剖面（1981年9月-1985年1月）。同时,为研究LaCoste ET-20和ET-21重力仪的格值系统,建立了一条由17台LaCoste G型和2台LaCoste D型重力仪观测的重力垂直基线。在基线上标定的结果表明,ET-21重力仪的格值大了1％。由标定得到的格值计算剖面上各测站的潮汐因子,经海潮改正后,接近Wahr模型值,振幅因子的残差:O₁波小于0.3μGal,M₂波小于0.4μGal。但是上海和拉萨的观测经海潮改正后,相位迟后有很大的改善,振幅因子却更偏离于模型值,其潮汐异常主要是近海的海潮模型不完善,以及在海潮计算中,所采用的地球模型未考虑地壳与上地幔的横向不均匀性所引起。     

Amplification of the storm surges in shallow waters of the Pertuis Charentais (Bay of Biscay,France)

The Pertuis Charentais are shallow coastal embayments formed by the islands of Oleron and Re in the north-eastern Bay of Biscay. The low-lying coasts of the Pertuis Charentais are susceptible to extensive flooding caused by the storm surges generated in the North Atlantic. Numerical modelling of the 24 October 1999 surge event is performed in the present study in order to elucidate the impact of the wind-wave-tide-surge interactions on the surge propagation in the Pertuis Charentais. A 2D numerical model is constructed to simulate the wave and tide-surge propagation on a high-resolution finite-element grid by using the TELEMAC and TOMAWAC software. The effect of the wave-induced enhancement on the sea surface drag and on the bottom friction is evaluated by using the models of Janssen (1991) and Christoffersen and Jonsson (1985), respectively. The radiation stress is estimated by employing the approach of Longuet-Higgins and Stewart (1964). It is demonstrated that the peak surge in the night on 23–24 October has been amplified inside the Pertuis Charentais by about 20 cm due to the wind-wave interactions with the tide-surge currents. These interactions are strongest at the entrance to the Pertuis Charentais where the sea surface drag coefficient is significantly increased by the wind-wave coupling. The effect of the wave-tide-surge interactions is large enough to be included in the flood forecasting systems of this region.     

Mechanical Response of Saturated Geological Rock Mass under Tidal Force

In this paper,the mechanical response of saturated geological rock under tidal force is explored by poroelastic theory.First,we use the free energy formula of saturated rock under a tidal force to study the relationships of pore pressure with stress,and stress with strain.Then we analyze the relationship between rock strain and tidal potential by the equilibrium differential equations of saturated rock under tidal force.Finally,we derive the physical relationship between the two parameters (pore pressure and tidal mean stress) of saturated rock and tidal potential.The relationship shows that:pore pressure is directly proportional with tidal potential,but tidal mean stress of saturated rock is inversely proportional with tidal potential.The ratio coefficient is related not only to the Lame coefficients of rock skeletons,but also to the Biot modulus.By using this model to analyze observational well water level of C-18 well which locates in Huili,Sichuan Province,the well level response coefficient (D) was estimated.This way,we derive the Skempton coefficient (B),the coefficient A and C which refer to the response coefficients of pore pressure and tidal stress to tidal potential respectively.Then we compare the differences among each coefficient in coupling and uncoupling conditions.It shows that for saturated rocks,the response of stress and pore pressure to earth tides is a product of coupling,and it is necessary to take into account the coupling effect when we study the mechanical response.The model will provide the basis not only for the study of mechanics and hydrodynamics of well-confined aquifer systems,and the mechanics of faulting under tidal force,but also for quantitative research of the triggering mechanism of tidal forces.     

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     

Effect of channel deepening on tidal flow and sediment transport: part I—sandy channels

Natural tidal channels often need deepening for navigation purposes (to facilitate larger vessels). Deepening often leads to tidal amplification, salinity intrusion, and increasing sand and mud import. These effects can be modelled and studied by using detailed 3D models. Reliable simplified models for a first quick evaluation are however lacking. This paper presents a simplified model for sand transport in prismatic and converging tidal channels. The simplified model is a local model neglecting horizontal sand transport gradients. The latter can be included by coupling (as post-processing) the simplified model to a 2DH or 3D flow model. Basic sand transport processes in stratified tidal flow are studied based on the typical example of the tidal Rotterdam Waterway in The Netherlands. The objective is to gain quantitative understanding of the effects of channel deepening on tidal penetration, salinity intrusion, tidal asymmetry, residual density-driven flow, and the net tide-integrated sand transport. We firstly study the most relevant tidal parameters at the mouth and along the channel with simple linear tidal models and numerical 2DH and 3D tidal models. We then present a simplified model describing the transport of sand (TSAND) in tidal channels. The TSAND model can be used to compute the variation of the depth-integrated suspended sand transport and total sand transport (incl. bed-load transport) over the tidal cycle. The model can either be used in stand-alone mode or with computed near-bed velocities from a 3D hydrodynamic model as input data.     

Ice-induced seasonal variability of tidal constants in the Arctic Ocean

The results for three-dimensional (3D) winter and summer tidal flows in the homogeneous Arctic Ocean, obtained with the use of a modified version of the 3D finite-element hydrothermodynamic model QUODDY-4, are presented. It is shown that seasonal variability of the M₂ tidal constants (amplitudes and phases of tidal sea surface level elevations) in the Central and Canadian parts of the Arctic Ocean is less than the error in the predicted tidal sea surface level elevations. This means that the seasonal variability can be neglected at least as a first approximation. A different situation is encountered in the Siberian continental shelf, where seasonal changes of tidal amplitude are ±5 cm, while those of tidal phase vary from 15° to several tens of degrees.     

Indirect determination of the heat budget of tidal flats

A method is presented to calculate indirectly the heat budget of a tidal flat area from downstream observations of temperature and horizontal velocity in a tidal channel. It is only necessary to establish a relationship between the velocity and the volume flux. Then the heat budget of the upstream region is determined by integrating the heat flux over one tide. The proposed method is applied to long-term measurements obtained in 2004 at two sites in a tidal channel in the Hörnum Basin, German Wadden Sea. At the site located farther downstream in the channel, the upstream catchment area is diagnosed to export heat (heat gain in the interior) from March to August, while import is diagnosed for the same period of time at the other upstream site. From September to November the situation is reversed. An analytical estimate suggests that the sign of the budget is controlled by the tidal prism and the length of the dry-falling period of the flats in the respective upstream region. In addition, a simple model is developed which can be used to determine the integral bottom heat flux of the tidal flats.     

Determination of the freshwater budget of tidal flats from measurements near a tidal inlet

The freshwater budget of a tidal flat area is evaluated from long-term hydrographic time series from an observation pole positioned in a tidal channel in the Hörnum Basin (Germany). For each tidal cycle, the freshwater budget is calculated from the total imported and exported water volumes and the corresponding mean densities. The variability of the budget on a tidal scale is characterised by a period of twice the tidal period, exhibiting a minimum when the tidal flats are dry around daylight hours during the foregoing low tide, and a maximum when low tide occurs at night; enhanced evaporation on the flats at daylight hours is identified as the driving process. On the average over one year, while winter observations are missing, the freshwater budget is negative for the years 2002–2005 and positive only for 2006. The interannual mean is negative and amounts to a freshwater loss of about 2 mm day⁻¹, although the large-scale climate in this region is humid. The results demonstrate that the bulk parametrisations for the latent and sensible heat flux between the ocean and the atmosphere must not be applied for the tidelands.     

Growth of large-scale bed forms due to storm-driven and tidal currents: a model approach

An idealized morphodynamic model is used to gain further understanding about the formation and characteristics of shoreface-connected sand ridges and tidal sand banks on the continental shelf. The model consists of the 2D shallow water equations, supplemented with a sediment transport formulation and describes the initial feedback between currents and small amplitude bed forms. The behaviour of bed forms during both storm and fair weather conditions is analyzed. This is relevant in case of coastal seas characterized by tidal motion, where the latter causes continuous transport of sediment as bed load.The new aspects of this work are the incorporation of both steady and tidal currents (represented by an M₂ and M₄ component) in the external forcing, in combination with dominant suspended sediment transport during storms. The results indicate that the dynamics during storms and fair weather strongly differ, causing different types of bed forms to develop. Shoreface-connected sand ridges mainly form during storm conditions, whereas if fair weather conditions prevail the more offshore located tidal sand banks develop. Including the M₄ tide changes the properties of the bed forms, such as growth rates and migration speeds, due to tidal asymmetry. Finally a probabilistic formulation of the storm and fair weather realization of the model is used to find conditions for which both types of large-scale bed forms occur simultaneously. These conditions turn out to be a low storm fraction and the presence strong tidal currents in combination with strong steady currents during storms.     

Net sediment transport in tidal basins: quantifying the tidal barotropic mechanisms in a unified framework

Net sediment transport in tidal basins is a subtle imbalance between large fluxes produced by the flood/ebb alternation. The imbalance arises from several mechanisms of suspended transport. Lag effects and tidal asymmetries are regarded as dominant, but defined in different frames of reference (Lagrangian and Eulerian, respectively). A quantitative ranking of their effectiveness is therefore missing. Furthermore, although wind waves are recognized as crucial for tidal flats’ morphodynamics, a systematic analysis of the interaction with tidal mechanisms has not been carried out so far. We review the tide-induced barotropic mechanisms and discuss the shortcomings of their current classification for numerical process-based models. Hence, we conceive a unified Eulerian framework accounting for wave-induced resuspension. A new methodology is proposed to decompose the sediment fluxes accordingly, which is applicable without needing (semi-) analytical approximations. The approach is tested with a one-dimensional model of the Vlie basin, Wadden Sea (The Netherlands). Results show that lag-driven transport is dominant for the finer fractions (silt and mud). In absence of waves, net sediment fluxes are landward and spatial (advective) lag effects are dominant. In presence of waves, sediment can be exported from the tidal flats and temporal (local) lag effects are dominant. Conversely, sand transport is dominated by the asymmetry of peak ebb/flood velocities. We show that the direction of lag-driven transport can be estimated by the gradient of hydrodynamic energy. In agreement with previous studies, our results support the conceptualization of tidal flats’ equilibrium as a simplified balance between tidal mechanisms and wave resuspension.     

The impact of the spatial variability in bottom roughness on tidal dynamics and energetics, a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.     

引潮力作用下饱和地质岩体的力学响应

本文应用孔隙弹性理论,探讨了引潮力作用下饱和地质岩体的力学响应.首先通过引潮力作用下饱和岩体的自由能表达式,得到岩体孔压与应力、应力与应变之间的关系;然后从引潮力作用下饱和岩体的平衡微分方程出发,结合流-固耦合理论,分析了饱水岩体应变与引潮位之间的关系;最后推导出饱和岩体的两大力学物理量--孔压和潮汐应力(平均应力)与引潮位之间的物理关系.模型表明:饱和岩体孔压与引潮位成反比,平均潮汐应力与引潮位成正比;比例系数不仅与岩体骨架的Lame系数有关,而且与Biot模量有关.将模型应用于会理川-18井水位变化分析,估计出水位响应系数D,并以此为基础,求得岩体孔压、潮汐应力与引潮位的相关系数(A和C)及Skempton系数B.最后对比分析了耦合条件下与不考虑耦合时得到的各参数之间的差异,分析表明:对饱和地质岩体而言,应力、孔压对引潮力的响应是流-固耦合作用的产物;研究其力学响应时必须充分考虑耦合效应.模型的建立,为研究引潮力作用下井-承压含水层系统力学、水动力学、与地震有关的断层力学以及引潮力触发机制的定量研究提供了基础.     

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.     

Tidal ice drift and ice-generated changes in the tidal dynamics/energetics on the Siberian continental shelf

Tidal ice drift is regarded as an element of the 3D tidal dynamics on the Siberian continental shelf. Two cases are considered: (1) when sea ice is immobile (in a horizontal plane), so that ice-induced changes of tidal characteristics may be treated as if they are limiting, and (2) when sea ice is moveable and internal stresses in the ice cover are described by a viscous-elastic rheology. It is shown that sea ice does not lead to radical changes of the tidal and energetic regimes, although their quantitative changes may be quite significant. In general, the ice-induced influence on the tidal dynamics is less than that on the tidal energetics. Therefore, the commonly accepted assumption that this influence may be viewed as being negligible is justified only partially. We present model results for tidal ice drift parameters—its magnitude, direction, the amplitude of tidal variations of ice concentration and the pressure of ice compression—as well as for ice-induced changes of tidal characteristics and the residual tidal ice drift. Partial attention is given to revealing the zones of ice compression–rarefaction, that is of importance in Arctic navigation.     

The impact of the spatial variability in bottom roughness on tidal dynamics and energetics,a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.

     

A coupled oscillator model of shelf and ocean tides

The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic _M2$M_2$ amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power consumption.     

A model study of tidal distributions in the Celtic and Irish Sea regions determined with finite volume and finite element models

An unstructured mesh tidal model of the west coast of Britain, covering the Celtic Sea and Irish Sea is used to compare tidal distributions computed with finite element (FE) and finite volume (FV) models. Both models cover an identical region, use the same mesh, and have topography and tidal boundary forcing from a finite difference model that can reproduce the tides in the region. By this means, solutions from both models can be compared without any bias towards one model or another. Two-dimensional calculations show that for a given friction coefficient, there is more damping in the FV model than the FE model. As bottom friction coefficient is reduced, the two models show comparable changes in tidal distributions. In terms of mesh resolution, calculations show that for the M₂ tide, the mesh is sufficiently fine to yield an accurate solution over the whole domain. However, in terms of higher harmonics of the tide, in particular the M₆ component, its small-scale variability in near-shore regions which is comparable to the mesh of the model, suggests that the mesh resolution is insufficient in the near-coastal regions. Even with a finer mesh in these areas, without detailed bottom topography and a spatial varying friction depending on bed types and bed forms, which is not available, model skill would probably not be improved. In addition in the near-shore region, as shown in the literature, the solution is sensitive to the form of the wetting/drying algorithm used in the model. Calculations with a 3D version of the FV model show that for a given value of k, damping is reduced compared to the 2D version due to the differences in bed stress formulation, with the 3D model yielding an accurate tidal distribution over the region.     

Generation of overtides and compound tides in Amazon estuary

Tidal propagation in estuaries is affected by friction and fresh water discharge, besides changes in the depth and morphology of the channel. Main distortions imply variations in the mean water level and asymmetry. Tidal asymmetry can be important as a mechanism for sediment accumulation and turbidity maximum formation in estuaries, while mean water level changes can affect navigation depths. Data from several gauges stations from the Amazon estuary and the adjacent coast were analyzed and a 2DH hydrodynamic model was configured in a domain covering the continental shelf up to the last section of the river where the tidal signature is observed. Based on data, theoretical and numerical results, the various influences in the generation of estuarine harmonics are presented, including that of fresh water discharge. It is shown that the main overtide, M₄, derived from the most important astronomic component in the Amazon estuary, M₂, is responsible for the tidal wave asymmetry. This harmonic has its maximum amplitude at the mouth, where minimum depths are found, and then decreases while tide propagates inside the estuary. Also, the numerical results show that the discharge does not affect water level asymmetry; however, the Amazon river discharge plays an important role in the behavior of the horizontal tide. The main compound tide in Amazon estuary, Msf, generated from the combination of the M₂ and S₂, can be strong enough to provoke neap low waters lower than spring ones. The results show this component increasing while going upstream in the estuary, reaching a maximum and then slightly decaying.