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.     

Progress in numerical modeling of subducting plate dynamics

The core concerns of plate tectonics theory are the dynamics of subducting plates, which can be studied by integrating multidisciplinary fields such as seismology, mineral physics, rock geochemistry, geological formation studies, sedimentology, and numerical simulations. By establishing a theoretical model and solving it with numerical methods, one can replicate the dynamic effects of a subducting plate, quantifying its evolution and the surface response. Simulations can also explain the observations and experimental results of other disciplines. Therefore, numerical models are among the most important tools for studying the dynamics of subducting plates. This paper provides a review on recent advances in the numerical modeling of subducting plate dynamics. It covers various aspects, namely, the origin of plate tectonics, the initiation process and thermal structure of subducting slab, and the main subduction slab dynamics in the upper mantle, mantle transition zone, and lower mantle. The results of numerical models are based on the theoretical equations of mass, momentum, and energy conservation. To better understand the dynamic progress of subducting plates, the simulation results must be verified in comparisons with the results from natural observations by geology, geophysics and geochemistry. With the substantial increase in computing power and continuous improvement of simulation methods, numerical models will become a more accurate and efficient means of studying the frontier issues of Earth sciences, including subducting plate dynamics.     

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.     

Desert pavement dynamics: numerical modeling and field‐based calibration

Desert pavements are widely used as a relative surface‐dating tool because they are progressively better developed on surfaces ranging from thousands to hundreds of thousands of years in age. Recent work, however, has highlighted the dynamic nature of pavements and undermined their use as surface‐age indicators. Quade (2001) proposed that latest Pleistocene vegetation advances destroyed all Mojave Desert pavements above 400 m elevation, making all such pavements Holocene in age. In an effort to reconcile young‐pavement evidence with their widespread use as Pleistocene surface‐age indicators, we developed a numerical model based on the classic conceptual model in which pavements co‐evolve with their underlying eolian epipedons over millennial timescales. In this co‐evolutionary process, fine‐grained eolian deposition and A_v‐horizon development within the eolian epipedon promotes surface clast motion and pavement development, enhancing the eolian‐sediment‐trapping ability of the pavement in a positive feedback. Model results illustrate the multi‐scale nature of pavement dynamics: pavements may require tens of thousands of years to fully develop from a newly abandoned alluvial surface, but may heal over timescales of decades to centuries if a mature eolian epipedon is present. As such, there is no inconsistency between rapid pavement healing and a Pleistocene age for the underlying alluvial surface. To calibrate the model, we conducted surficial geologic mapping and pavement‐sedimentological analysis on two desert piedmonts. Our study areas include both proximal and distal fan environments, illustrating the role of parent‐material texture in controlling the mode of pavement formation. Using available geochronology, our work provides a rigorous calibration of pavement formation rates in our study areas and provides evidence supporting the use of pavements as local relative surface‐age indicators over Holocene to late Pleistocene timescales. Copyright © 2007 John Wiley & Sons, Ltd.     

Mapping dune dynamics by InSAR coherence

It is generally held that subtle changes in sandy environments are very difficult to detect in imagery. Nonetheless, this study demonstrates how synthetic aperture radar (SAR) interferometric decorrelation can be used to identify changes in individual sand dunes. The use of coherence maps over time facilitates the analysis of dune dynamics, both temporally and spatially. The Ashdod‐Nizzanim coastal dunes, along the southern coastal plain of Israel, were chosen as an illustrative example of the analysis of dune dynamics. High‐resolution TerraSAR‐X (TSX) radar images covering the entire research area were acquired for the period February to July 2012, together with meteorology data (wind and rain) for the area. The coherence results enabled the stability of individual dunes to be described as a function of time. It was found that the dune crests were more stable than the windward slopes and that the degree of stability was dependent on the distance of the dune from the sea. The results of this study show the potential of using interferometric synthetic aperture radar (InSAR) decorrelation for aeolian studies, even in areas characterized by low coherence. Copyright © 2017 John Wiley & Sons, Ltd.     

Baroclinic tidal flows and inundation processes in Cook Inlet, Alaska: numerical modeling and satellite observations

A wetting and drying (WAD) algorithm is implemented in a baroclinic three-dimensional ocean circulation model of Cook Inlet, Alaska, where large tidal ranges (≈10 m) regularly expose extensive mudflats. The model includes tides and wind- and buoyancy-induced flows. In the upper Inlet, the model successfully simulates large amplification of tides and propagation of fast (3 ∼ 4 m s⁻¹) tidal bores over shallow mudflats. The simulated return flows during ebb expose large areas (∼100 km²) of the mudflats. Medium-resolution (250- and 500-m) images obtained from the moderate resolution imaging spectroradiometer (MODIS) instruments aboard the Terra and Aqua satellites were used to verify the model results by identifying the location, extent, and temporal changes of the exposed mudflat regions. The results demonstrate the value of operational, medium-resolution remote sensing data in evaluating the WAD model. Sensitivity tests show that WAD produces approximately 20% larger tidal amplitude and 10% slower phase than the corresponding experiment without WAD. In the deep channel of the central Inlet, the confluence of saline water of the lower Inlet with brackish water from rivers and melting ice from land around the upper Inlet produces a salinity front. At the simulated front, strong vertical circulation cells and surface convergence and currents develop, especially during the flood. The characteristics resemble those of “rip tides” often observed in this region.     

The effect of asymmetric dune roughness on tidal asymmetry in the Weser estuary

The bed of estuaries is often characterized by ripples and dunes of varying size. Whereas smaller bedforms adapt their morphological shape to the oscillating tidal currents, large compound dunes (here: asymmetric tidal dunes) remain stable for periods longer than a tidal cycle. Bedforms constitute a form roughness, that is, hydraulic flow resistance, which has a large-scale effect on tidal asymmetry and, hence, on hydrodynamics, sediment transport, and morphodynamics of estuaries and coastal seas. Flow separation behind the dune crest and recirculation on the steep downstream side result in turbulence and energy loss. Since the energy dissipation can be related to the dune lee slope angle, asymmetric dune shapes induce variable flow resistance during ebb and flood phases. Here, a noncalibrated numerical model has been applied to analyze the large-scale effect of symmetric and asymmetric dune shapes on estuarine tidal asymmetry evaluated by residual bed load sediment transport at the Weser estuary, Germany. Scenario simulations were performed with parameterized bed roughness of symmetric and asymmetric dune shapes and without dune roughness. The spatiotemporal interaction of distinct dune shapes with the main drivers of estuarine sediment and morphodynamics, that is, river discharge and tidal energy, is shown to be complex but substantial. The contrasting effects of flood- and ebb-oriented asymmetric dunes on residual bed load transport rates and directions are estimated to be of a similar importance as the controls of seasonal changes of discharge on these net sediment fluxes at the Lower Weser estuary. This corroborates the need to consider dune-induced directional bed roughness in numerical models of estuarine and tidal environments.     

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.     

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.     

Effect of non-migrating bars on dune dynamics in a lowland river

As dunes and larger-scale bed forms such as bars coexist in rivers, the question arises whether dune dynamics are influenced by interaction with the underlying bed topography. The present study aims to establish the degree to which dune characteristics in two and three dimensions are influenced by an underlying topography dominated by non-migrating bars. As a case study, a 20 km stretch in the Waal River in the Netherlands is selected, which represents a sand-bed lowland river. At this location, longitudinal training dams (LTDs) have recently been constructed to ensure sufficient navigation depth during periods with low water levels, and to reduce flood risk. By using data covering 2-year-long periods before and after LTD construction, the robustness of the results is investigated. Before LTD construction, dune characteristics show large variability both spatially and temporally, with dunes being longer, lower, less steep and having a lower lee side angle when they are located on bar tops. The correlation between dune characteristics and the underlying bed topography is disrupted by unsteady conditions for which the dunes are in a state of transition. The bar pattern causes tilting of dune crest lines, which may result from a transverse gradient in bedload sediment transport. As a result of LTD construction, the hydraulic and morphological conditions have changed significantly. Despite this, the main conclusions still hold, which strengthens the validity of the results. ©2020 The Authors. Earth Surface Processes and Landforms published by 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.     

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.     

多震源地震正演数值模拟技术

常规地震采集技术因受相邻时间激发炮之间时间间隔的制约而存在采集周期过长,采集成本过高的问题,而多震源同步激发地震采集技术可以克服这方面的缺陷,但存在着波场过于复杂的问题,地震正演模拟技术可以帮助我们提高对这种复杂波场的认识水平,为此采用2D弹性波方程交错网格高阶有限差分格式,开发了多震源同步激发波场正演数值模拟技术,能够模拟任意多个同步激发震源的弹性波波场,震源函数可以是雷克子波,也可以是可控震源扫描信号,且同步激发震源之间可以有随机时差.模型试算结果分析表明,该技术既是一项高精度的多震源正演模拟技术,也是一项高效率的地震正演数值模拟技术.     

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.     

Inverse modeling of coastal aquifers using tidal response and hydraulic tests

Remediation of contaminated aquifers demands a reliable characterization of hydraulic connectivity patterns. Hydraulic diffusivity is possibly the best indicator of connectivity. It can be derived using the tidal response method (TRM), which is based on fitting observations to a closed-form solution. Unfortunately, the conventional TRM assumes homogeneity. The objective of this study was to overcome this limitation and use tidal response to identify preferential flowpaths. Additionally, the procedure requires joint inversion with hydraulic test data. These provide further information on connectivity and are needed to resolve diffusivity into transmissivity and storage coefficient. Spatial variability is characterized using the regularized pilot points method. Actual application may be complicated by the need to filter tidal effects from the response to pumping and by the need to deal with different types of data, which we have addressed using maximum likelihood methods. Application to a contaminated artificial coastal fill leads to flowpaths that are consistent with the materials used during construction and to solute transport predictions that compare well with observations. We conclude that tidal response can be used to identify connectivity patterns. As such, it should be useful when designing measures to control sea water intrusion.     

Fine grid tidal modeling of the Yellow and East China Seas

A fine grid tidal modeling experiment is carried out in order to investigate the tidal regimes for major five tidal constituents, the nonlinear tidal phenomena in terms of M₄ and MS₄ generation, and the independent tide by the tide generating force in the Yellow and East China Seas (YECS). In this study a two-dimensional numerical model based upon a subgrid-scale (SGS) stress modeling technique is used with the tide generating force included. The model was validated with recently observed tide and current data. The calculated tidal charts for tidal elevation show a generally good agreement with existing ones, with more accurate feature of the M₂ cotidal chart in comparison with both the observed data and the existing tidal charts. A careful comparison of the computed diurnal amplitude with observations suggests that the diurnal constituents seem to be overdamped especially in the Kyunggi Bay region, for the case when quadratic bottom friction law is used.Propagation features of the M₄(MS₄) tides are discussed in the YECS, based upon the analyses of the observed and calculated results. The amphidromic system of the M₄ is quite complicated and one noticeable characteristic is that the propagation direction of the M₄ tidal wave along the west coast of Korean peninsula is opposite to that of the M₂ tidal wave. This result coincides with observations. The propagation feature of the MS₄ is almost similar to that of the M₄, but with lesser amplitude. The responses of the M₄ tidal features to momentum diffusion term and depth-dependent form of the friction coefficient are also discussed.It is also shown that when the independent tide (Defant, 1960) arising from tide generating force (TGF) coexists with tidal waves (co-oscillating tide) arising from external boundary forcing, the TGF tidal waves are dissipated and their amphidromes tend to move westward. This may be interpreted as a process whereby the incident and reflected TGF tidal waves are damped by co-oscillating tide arising from external force at open boundaries. The TGF amplitude is found to be up to 10 cm and 4 cm in the Kyunggi Bay for the M₂ and S₂ constituents while those for all diurnal constituents are less than 1 cm over the entire model domain.     

Molecular dynamics modeling of stishovite

A Morse-stretch potential charge equilibrium force field for silica system has been employed to simulate the thermodynamics of stishovite with the molecular dynamics (MD) method. The equation of state, thermal expansivity and melting curve of stishovite have been obtained. This simple force field yielded results in accordance with the static and dynamic experiments. The stishovite melting simulation appears to validate the interpretation of superheating of the solid along the Hugoniot in the shock melting experiments. MD simulations show that the thermal expansivity of stishovite at lowermost mantle conditions is a weak function of temperature. The phase diagram of silica up to the mega bar regime is proposed based on the experimental and theoretical studies. The related physical and geophysical implications are addressed.     

Population dynamics of earthquakes and mathematical modeling

We present a mathematical model that describes temporal variations of earthquakes. This model is represented as $$dn(t)/dt = n(t)\left[ {\alpha - \beta n(t) - \int_{ - \infty }^t {n(s)h(t - s)ds} } \right].$$ Heren(t) shows the numberof earthquakes per unit time in a certain region. α and β are constants. The functionh(t) denotes the hysteresis effect of the earthquake occurrences and can take the following forms depending on the physical conditions of the crusts; (A)h(t)=0: the equation represents a logistic type increase or decrease and approaches a stationary state asymptotically. This describes aftershock series of large earthquakes and earthquake swarms of large scale such as the Wakayama and Matsushiro swarms in Japan; (B)h(t)=constant (β=0): frequencyn(t) increases initially and then decreases gradually and shows some kind of volcanic swarms; (C)h(t) = κ · {exp(?γ₁ t) ? exp(γ₂ t)}, (γ₂ > γ₁): this denotes time delay effects and the model shows periodic patterns of bursts or “rhythms” of earthquakes, which are observed in earthquake swarms. When external effects are taken into consideration, the model is further generalized and can describe various seismic patterns. These effects represent various influences of the circumstances like the earth tide and fluctuations of plate motions, etc. Whenh(t) takes type (A) and the external effect is random, the equation displays repetitive random patterns with bursts. Particularly interesting cases may be those whenh(t) is type (C) and the external force is periodic like the earth tide. Various nonperiodic as well as periodic patterns of earthquakes appear. These are the phenomena of “chaos” and “entrainment”, etc. and can be commonly observed. Varieties of actual earthquake patterns seem to be, at least partly, explained by the nonlinear coupling between the tidal forces and autonomous rhythms of earthquakes.     

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.