A numerical study of equilibrium states in tidal network morphodynamics

The long-term morphodynamic evolution of tidal networks on tidal flats is investigated using a two-dimensional numerical model. We explore the physical processes related to the development of the morphology and the presence of equilibrium configurations. Tidal networks are simulated over a rectangular domain representing a tidal platform, a different setting compared to estuaries (subject to riverine influence) and lagoons (offshore bars constricting the flow). In the early and middle phases of the tidal network evolution, large sediment patches with rhombus-like shape form and gradually migrate in the flood direction, even though the overall sediment flux is ebb-directed. A cross-section-averaged “equilibrium” state is asymptotically approached after about 500 years. The area and peak discharge of the lower flat cross-sections at year 500 approximately show a 1:1 relationship, which is in agreement with field observations. We also show that model results are consistent with the Q-A relationship (peak discharge Q versus cross-sectional area A), which is obtained under the assumption of a constant Chézy friction.     

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.     

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.     

Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

In this paper, we describe carefully conducted numerical experiments, in which a dense salt solution vertically displaces fresh water in a stable manner. The two-dimensional porous media are weakly heterogeneous at a small scale. The purpose of these simulations, conducted for a range of density differences, is to obtain accurate concentration profiles that can be used to validate nonlinear models for high-concentration-gradient dispersion. In this part we focus on convergence of the computations, in numerical and statistical sense, to ensure that the uncertainty in the results is small enough.Concentration variances are computed, which give estimates of the uncertainty in local concentration values. These local variations decrease with increasing density contrast. For tracer transport, obtained longitudinal dispersivities are in accordance with analytical findings. In the case of high-density contrasts, stabilizing gravity forces counteract the growth of dispersive fingers, decreasing the effective width of the transition zone. For small log-permeability variances, the decrease of the apparent dispersivity that is found is in agreement with laboratory results for homogeneous columns.     

A numerical study on the basin edge effect on soil amplification

In this paper a numerical study on the effects of the basin edge on the dynamic behavior of the model basins are investigated. For this purpose a range of bedrock inclinations at the valley sides from slighter $10^{\circ }$ and $20^{\circ }$ to steeper $30^{\circ }$ and $40^{\circ }$ are selected. A numerical study using nonlinear code which utilizes appropriate static and dynamic boundary conditions, and includes hysteresis damping formulation based on user defined degradation curves is conducted utilizing two sandy and clayey materials. Using several different real earthquake motions provide opportunity for the assessment of the site response to the variation of the motion intensity. The analyses results are presented in the form of the acceleration and spectral acceleration amplification curves. Also, by conducting 1D analyses along the valley the aggravation curve for every case are evaluated and discussed. It was seen that variation of the bedrock inclination not only affects the peaks of the spectral amplification curves, but also the position of the maximums of the curves on the valley surface are changed. Also, the frequency domain results show that different parts of the valleys are sensitive to different periods. While the lateral parts are sensitive to lower periods, the maximum amplification of the inner parts takes place at higher periods. Based on results the 2D behavior not only is dominant at the latreal parts of the valley, but also affects the behavior of the inner parts. Also, the use of the 1D analyes for the estimation of the 2D behavior remains insufficient. Finally, the results of this research show the important effect of the motion intensity on the 2D behavior of the valley specially on the increase of the resonance period at higher period.     

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     

Analytical solutions for tidal propagation in a rectangular basin

The tidal propagation in a rectangular basin of an estuary has been studied in this paper. The dynamic response of the tidal current and elevation inside the basin has been obtained using the concept of Kelvin waves and spectrum of Poincare waves. In this study, we have found that initial tidal elevations are amplified near the closed end of the basin or at the tidal barrier site.     

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.     

A numerical method to calculate the electromagnetic field of a horizontal current dipole

Summary A computer program is described to calculate the field of an oscillating current dipole over a horizontally stratified medium for the quasi-static case. Multi-layer master curves for frequency sounding can be calculated with this program. Examples of these curves are presented.Contribution No. 90 of the Geophysical Institute, Swiss Federal Institute of Technology, Zürich.     

Exact transverse macro dispersion coefficients for transport in heterogeneous porous media

We study transport through heterogeneous media. We derive the exact large scale transport equation. The macro dispersion coefficients are determined by additional partial differential equations. In the case of infinite Peclet numbers, we present explicit results for the transverse macro dispersion coefficients. In two spatial dimensions, we demonstrate that the transverse macro dispersion coefficient is zero. The result is not limited on lowest order perturbation theory approximations but is an exact result. However, the situation in three spatial dimensions is very different: The transverse macro dispersion coefficients are finite – a result which is confirmed by numerical simulations we performed.     

3-D physical model in strong ground motion numerical simulation： A case study of Kunming basin

Seismic hazard assessment based on urban active faults can provide scientific bases for city planning and projectconstruction,while numerical simulation of strong ground motion is an important method for seismic hazard pre-diction and assessment.A 3-D physical model in conformity with real strata configuration of(mainly)the Quater-nary is a prerequisite to ensure the reliability of the simulation results.In this paper,we give a detailed account ofthe technical scheme and process for creating a 3-D physical model in Kunming basin.The data used are synthe-sized from seismogeological data,borehole data,topographic data,digital elevation mode(DEM)data,seismicexploration results and wave velocity measurements.Stratigraphic division is based mainly on shear wave velocity,with strata sequence taken into consideration.The model construction is finally accomplished with ArcGIS andmany relevant programming techniques via layer-by-layer stacking(in depth direction)of the adjacent mediuminterfaces(meshes).Meanwhile,a database of 3-D physical models is set up,which provides model data and pa-rameters for strong ground motion simulation.Some processing methods and significant issues are also addressedin the paper in accordance with different types of exploration and experimental data.     

Experimental and numerical modelling of sedimentation in a rectangular shallow basin

Numerical simulation of flows in shallow reservoirs has to be checked for its consistency in predicting real flow conditions and sedimentation patterns. Typical flow patterns may exhibit flow separation at the inlet, accompanied by several recirculation and stagnation areas all over the reservoir surface. The aim of the present research project is to study the influence of the geometry of a reservoir on sediment transport and deposition numerically and experimentally, focusing on a prototype reservoir depth between 5 and 15 m as well as suspended sediment transport.
A series of numerical simulations is presented and compared with scaled laboratory experiments, with the objective of testing the sensitivity to different flow and sediment parameters and different turbulence closure schemes. Different scenarios are analyzed and a detailed comparison of preliminary laboratory tests and some selected simulations are presented.
The laboratory experiments show that suspended sediment transport and deposition are determined by the initial flow pattern and by the upstream and downstream boundary conditions. In the experiments, deposition in the rectangular basin systematically developed along the left bank, although inflow and outflow were positioned symmetrically along the centre of the basin. Three major horizontal eddies developed influencing the sediment deposition pattern. Although asymmetric flow patterns are privileged, a symmetric pattern can appear from time to time. This particular behaviour could also be reproduced by a two-dimensional depth-averaged flow and sediment transport model （CCHE2D）. The paper presents numerical simulations using different turbulence closure schemes （k-ε and eddy viscosity models）. In spite of the symmetric setup, these generally produced an asymmetric flow pattern that can easily switch sides depending on the assumptions made for the initial and boundary conditions. When using the laboratory experiment as a reference, the most reliable numerical results have been obtai     

南黄海残留盆地宏观分布特征研究

由于前新生代残留盆地具有埋深大、构造复杂的特点,采用综合地球物理研究方法成为圈划残留盆地宏观分布及预测残留盆地油气资源的重要方法技术．本文以南黄海地区为例,以重、磁数据为主体,以钻井、地震等高精度数据为先验信息做约束,采用带约束界面反演方法求取重力基底,同时根据求取的磁性基底计算了中、古生界的残余厚度,给出了前新生界残留盆地宏观分布特征．结合石油地质条件,圈划了油气资源有利区．研究结果表明南黄海北部坳陷北部和东北部中生界残余厚度较大,中部隆起与勿南沙隆起古生界残余厚度巨大,是较好的前新生代油气前景区．     

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.     

波场模拟中的数值频散分析与校正策略

波动方程有限差分法正演模拟,对认识地震波传播规律、进行地震属性研究、地震资料地质解释、储层评价等,均具有重要的理论和实际意义.但有限差分法本身固有存在着数值频散问题,数值频散在正演模拟中是一种严重的干扰,会降低波场模拟的精度与分辨率.针对TI介质波场模拟的交错网格有限差分方法,本文从空间网格离散、时间网格离散和算子近似等三个方面对其产生的数值频散进行了分析,并结合其他学者的研究成果给出了TI介质波场模拟中压制数值频散的方法与策略：在已知介质频散关系时,对差分算子可实施算子校正;通过提高差分方程的阶数来提高波场模拟精度;采用流体力学中守恒式方程的通量校正传输方法来压制波场模拟中的数值频散;在实际正演模拟时,采用交错网格高阶有限差分方程,不仅在空间上采用高阶差分,而且在时间上也要采用高阶差分,否则只在单一方向上（空间或时间）提高方程的阶数对压制数值频散也不会取得理想的效果.     

Computing near coastal tidal dynamics from observations and a numerical model

A two-dimensional vertically integrated model of the North Sea is used to compute the distribution of M₂ and M₄ tidal elevations and currents over the region. Comparison of computed and observed elevations and currents in the area shows that the model can accurately reproduce the M₂ tide in the North Sea, although there are difficulties with the M₄ tide particularly in the northern North Sea.Comparison between model and a large number of observations collected in a shallow water region off the east coast of England, revealed that the model can accurately reproduce the tides even in near coastal regions, where model resolution problems can occur. Comparisons of computed and observed M₂ tidal energy fluxes in this region, show that model and observations agree to within the order of 10% (the error associated with the necessary interpolation of the observations in order to compute the energy flux).The problem of computing energy dissipation in the area by subtracting the energy fluxes into and out of the region is shown to be ill-conditioned in that the energy dissipation in the area is comparable to the error in the energy flux. Consequently for the sea region considered here it is not meaningful to compare this energy budget with energy dissipation due to bottom friction.Energy dissipation for the whole of the North Sea is computed using the numerical model and the geographical distribution of dissipation due to bottom friction is given for the M₂ tide.     

Experiments with a numerical model of coastal currents and tidal mixing fronts

A three-dimensional numerical model is used to simulate the development of disturbances on shelf-sea coastal currents and fronts. The model, which has a free surface, uses a finite difference grid ☐ scheme based on sigma coordinates. It has a semi-implicit scheme for the barotropic flow and a hydrid advection scheme to retain sharp fronts. The results demonstrate that (i) eddy formation follows changes at the inflow of a coastal current, (ii) a simple radiation boundary condition at the outflow produces nearly identical results for different outflow boundary positions, (iii) eddy growth, with matching behaviour of surface and bottom fronts, follows a small displacement on a tidal mixing front and (iv) effects of friction and mixing can significantly alter the behaviour of the front and the relative strength of the cyclonic and anticyclonic eddies formed.     

Turbulence and mixing in a freshwater-influenced tidal bay: Observations and numerical modeling

In situ observations and numerical simulations of turbulence are essential to understanding vertical mixing processes and their dynamical controls on both physical and biogeochemical processes in coastal embayments. Using in situ data collected by bottom-mounted acoustic Doppler current profilers(ADCPs) and a free-falling microstructure profiler, as well as numerical simulations with a second-moment turbulence closure model, we studied turbulence and mixing in the Xiamen Bay, a freshwater-influenced tidal bay located at the west coast of the Taiwan Strait. Dynamically, the bay is driven predominantly by the M2 tide, and it is under a significant influence of the freshwater discharged from the Jiulong River. It is found that turbulence quantities such as the production and dissipation rates of the turbulent kinetic energy(TKE) were all subject to significant tidal variations, with a pronounced ebb-flood asymmetry. Turbulence was stronger during flood than ebb. During the flooding period, the whole water column was nearly well mixed with the depth-averaged TKE production rate and vertical eddy viscosity being up to 5?10?6 W kg?1 and 2?10?2 m2 s?1, respectively. In contrast, during the ebb strong turbulence was confined only to a 5?8 m thick bottom boundary layer, where turbulence intensity generally decreases with distance from the seafloor. Diagnosis of the potential energy anomaly showed that the ebb-flood asymmetry in turbulent dissipation and mixing was due mainly to tidal straining process as a result of the interaction between vertically shared tidal currents and horizontal density gradients. The role of vertical mixing in generating the asymmetry was secondary. A direct comparison of the modeled and observed turbulence quantities confirmed the applicability of the second-moment turbulence closure scheme in modeling turbulent processes in this weakly stratified tidally energetic environment, but also pointed out the necessity of further refinements of the model.     

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.