Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf.     

Propagation of Kelvin waves along irregular coastlines in finite-difference models

In this paper, we examine the behavior of internal Kelvin waves on an f-plane in finite-difference models using the Arakawa C-grid. The dependence of Kelvin wave phase speed on offshore grid resolution and propagation direction relative to the numerical grid is illustrated by numerical experiments for three different geometries: (1) Kelvin wave propagating along a straight coastline; (2) Kelvin wave propagating at a 45° angle to the numerical grid along a stairstep coastline with stairstep size equal to the grid spacing; (3) Kelvin wave propagating at a 45° angle to the numerical grid along a coarse resolution stairstep coastline with stairstep size greater than the grid spacing. It can be shown theoretically that the phase speed of a Kelvin wave propagating along a straight coastline on an Arakawa C-grid is equal to the analytical inviscid wave speed and is not dependent on offshore grid resolution. However, we found that finite-difference models considerably underestimate the Kelvin wave phase speed when the wave is propagating at an angle to the grid and the grid spacing is comparable with the Rossby deformation radius. In this case, the phase speed converges toward the correct value only as grid spacing decreases well below the Rossby radius. A grid spacing of one-fifth the Rossby radius was required to produce results for the stairstep boundary case comparable with the straight coast case. This effect does not appear to depend on the resolution of the coastline, but rather on the direction of wave propagation relative to the grid. This behavior is important for modeling internal Kelvin waves in realistic geometries where the Rossby radius is often comparable with the grid spacing, and the waves propagate along irregular coastlines.©1998 Published by Elsevier Science Limited. All rights reserved     

Revisiting the Basin-edge Effect at Kobe During the 1995 Hyogo-Ken Nanbu Earthquake

The basin edge effect, i.e., the interference of the direct S wave with the surface wave diffracted off the basin edge has been invoked by many authors to explain the damage distribution during the January 17, 1995 Hyogo-Ken Nanbu (Kobe) earthquake. Here we present the results of numerical experiments obtained with the spectral element method in 2-D geometry. Our results confirm that the amplification of horizontal motion close to the basin edge can be twice as large as the one measured in the center of the basin. This additional amplification is shown to depend strongly on the edge geometry and on frequency, due to physical dispersion of diffracted surface waves. In particular we obtain maximal amplification around 3 Hz, at frequencies critical for buildings.     

Long Wave Resonance in Tropical Oceans and Implications on Climate: the Atlantic Ocean

Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.     

Modelling the influence of spatially varying hydrodynamics on the cross-sectional stability of double inlet systems

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams. Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).     

Modelling the influence of spatially varying hydrodynamics on the cross-sectional stability of double inlet systems

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams.

Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).

     

Effects of waves on the initiation of headland-associated sandbanks

Linear sandbanks appear in the lee of coastal headlands where the hydrodynamics are dominated by strong tidal currents and the seabed is characterized by an abundance of sands. They may develop as symmetrical sandbanks on either sides of the headland or as an unique banner bank. The present study numerically investigates the combined effects of waves and tide on the initial development of headland-associated sandbanks. A morphological model based on the coupling of the wave propagation module SWAN (Simulating WAves Nearshore) with the three-dimensional circulation module COHERENS (COupled Hydrodynamical-Ecological model for REgioNal and Shelf seas) is applied to an idealized Gaussian shaped headland for waves conditions varying in heights and directions at the offshore boundary. The coupling considers the effects of the interactions between the wave and current bottom boundary layers, namely the enhanced levels of turbulence near the bottom and the increase of the total bottom shear stress. Waves substantially modify the initial development of sandbanks formed by suspension narrowing their width and reorienting them along the side of the headland. They weakly impact the morphogenesis of sandbanks by bedload favoring on a short-time scale the growth of symmetric circular-shaped features and a central depositional spit prolonging the headland tip. Waves of transverse directions toward the tip of the headland contribute to the initiation by suspension of a well-developed feature in the headland side of low energy limiting the seabed evolution in the exposed area.     

Maintenance of headland-associated linear sandbanks: modelling the secondary flows and sediment transport

Linear sandbanks are located globally in areas where there are strong currents and an abundance of sand. In the recent years, these sandbanks have become of strategic interest as a potential source of marine aggregates (sand and gravel) and mineral deposits. They form the seaward boundary of the nearshore zone and therefore are important for the stability of the coastal system. They also commonly reach the sea surface and thus pose a threat to navigation. Headland-associated linear sandbanks are a specific type of sandbanks which are located in the lee of coastal topographic features such as headlands and islands. Interaction between tidal currents and topographic features generate complex three-dimensional circulation patterns that significantly influence the distribution of sediments in the vicinity of the feature. Field and numerical model investigations of the three-dimensional flow structure have been undertaken on the Levillain Shoal, a headland-associated linear sandbank present in the lee of Cape Levillain (Shark Bay, Western Australia). The field data indicated the presence of secondary flows near the tip of the cape and around the bank which were re-produced in the numerical simulations. Numerical results have shown that residual eddies are not representative of the sediment transport and that secondary currents enhance the convergence of sediment towards the sandbank. Maintenance processes have been investigated. Sediment transport paths near the cape and the bank indicate that the sandbank is part of a sand circulation cell where the sand is circulating around the bank with exchanges between the sandbank and the headland.     

The formation of headland/island sandbanks

There are four extensive sandbanks in the vicinity of the Isle of Portland, a headland in the English Channel. The formation and maintenance of the two most prominent of these sandbanks (one on either side of the headland) can largely be explained by net bedload convergence, driven by instantaneous headland eddies generated by tidal flow past the headland. However, there are also two less prominent sandbanks (again, one on either side of the headland), which are not located in zones of bedload convergence. It is suggested here that these latter two sandbanks were formed when the Isle of Portland was isolated from the mainland by a tidal strait. Relative sea-level data and radiocarbon dates indicate that this would have occurred ca. 9–7 ka BP, prior to the closure of the strait by sedimentation. Tidal flow through this strait generated eddy systems in addition to the headland eddies, leading to the formation of associated headland/island sandbanks. At 7 ka BP, sedimentation resulted in closure of the strait, leading to the present-day headland configuration, and subsequent reworking of these now moribund sandbanks formed by the strait. A series of idealised morphological model experiments, parameterised using bedrock depths and glacial isostatic adjustment model output of relative sea level, are here used to simulate this hypothesised sequence of sandbank evolution over the Holocene. The results of the model experiments are corroborated by in situ observations of bedforms and sediment characteristics, and by acoustic Doppler current profiler (ADCP) data applied to predictions of bedload transport over the sandbanks. In addition to demonstrating the mechanism which leads to the formation of sandbanks by tidal flow through a strait, the model results show that upon subsequent closure of such a strait, these sandbanks will no longer be actively maintained, in contrast to sandbanks which are continuously maintained by headland eddies.     

Wind-induced baroclinic response of Lake Constance

We present results of various circulation scenarios for the wind-induced three-dimensional currents in Lake Constance, obtained with the aid of a semi-spectral semi-implicit finite difference code developed in Haidvogel et al. and Wang and Hutter. Internal Kelvin and Poincaré-type oscillations are demonstrated in the numerical results, whose periods depend upon the stratification and the geometry of the basin and agree well with measured data. By solving the eigenvalue problem of the linearized shallow water equations in the two-layered stratified Lake Constance, the interpretation of the oscillations as Kelvin and Poincaré-type waves is corroborated.     

Baroclinic,Kelvin and inertia-gravity waves in the barostrat instability experiment

The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment.     

Influence of the back-barrier basin length on the geometry of ebb-tidal deltas

The characteristics of ebb-tidal deltas are determined by the local hydrodynamics. The latter depend, among others, on the geometry of the adjacent back-barrier basin. Therefore, interventions in the back-barrier basin can affect the geometry of ebb-tidal deltas. In this study, the effect of the length of the back-barrier basin on the sand volume and spatial symmetry of ebb-tidal deltas is quantified with the use of a numerical model. It is found that the length of the back-barrier basin affects the tidal prism, the amplitude and phase of the primary tide and its overtides, and the residual currents that, together, determine the sand volume of the ebb-tidal delta. In particular, it is found that no unique relationship exists between tidal prism and sand volume of an ebb-tidal delta. The spatial symmetry of ebb-tidal deltas is also found to be affected by the length of the back-barrier basin. This is because the basin length determines the phase difference between alongshore and cross-shore tidal currents. The numerical model results give a possible explanation for the changes that are observed in the geometry of the ebb-tidal deltas that are located seaward of the Texel Inlet and Vlie Inlet after the closure of the Zuiderzee.     

Dynamical Control of Pacific Oceanic Low-frequency Variability on Western Boundary and Marginal Seas

The adjustment of sea surface height (SSH) around the coasts of the Japan/East Sea (JES) and the South China Sea (SCS) basins subjected to extratropical Pacific Oceanic low frequency variability is studied using a Kelvin-planetary wave model and a high resolution numerical model. It is found that the modulation of SSH around the coast of Japan is mainly determined by slow adjustment of planetary waves, which radiate from the west coast of Honshu and Hokkaido due to the coastal Kelvin wave. In contrast, the SSH modulation around the cost of the South China Sea basin is mainly determined by the coastal Kelvin wave, which transfers the anomalous SSH into the SCS via the Luzon Strait and out via the Mindoro Strait. The planetary waves radiating from the west coast of Palawan establish a nearly uniform SSH anomaly in the southern part of the SCS, bounded by an eastward jet at the latitude of the Mindoro Strait. Along the western boundary, SSH anomaly decreases almost linearly toward the south, in accordance with the changing local deformation radius. In these two marginal seas, the mean subtropical Pacific gyre circulation enhances SSH modulation induced by extratropical Pacific low frequency variability. Overall, the SSH adjustment in the JES and the SCS predicted by the analytical model agrees well with the numerical model simulation. Application of this model to interaction between these marginal seas and the open ocean is discussed.     

Hydromechanics for the formation and development of radial sandbanks (I)

Based upon the long-term observation of field data, a two-dimensional numerical model is applied to simulating the tidal flow covering from the neap tide to spring tide in the radial sandbank area in the southern Yellow Sea. From the development of tidal current ridges under the hydrodynamic action, multi-purpose analysis and study are carried out, which include the propagation process of tidal wave, the distributions of tidal wave energy rate and tidal range, the tidal ellipses and traces. It is shown that the tidal current is the major dynamic factor for the formation and development of the radial sandbanks, and the differences of tidal wave energy rate and current strength determine the distinct plane shapes of ridges and troughs in this region.     

Effect of advective and diffusive sediment transport on the formation of local and global bottom patterns in tidal embayments

Bathymetric field data of tidal basins reveal two main classes of bottom patterns: (1) tidal bars, located near the entrance of the basin (length scale determined by the embayment width) and (2) global channel-shoal patterns which scale with the basin length. Previous models were able to describe only either one of these patterns. In this paper it is shown that both of them can be investigated within the framework of an idealised model of a rectangular tidal embayment, with fixed side walls and an erodible bed. The water motion is described by the depth-averaged shallow-water equations and is forced by a prescribed vertical tide at the seaward entrance. Sediment is transported as suspended load and only realistic values of the bottom friction parameter are considered. By assuming the ratio of embayment length over tidal wave length to be small, the model allows for a morphodynamic equilibrium, characterised by a spatially uniform tide moving over a bottom which slopes upwards toward the landward boundary. This equilibrium is unstable for a range of values of the model parameters, such that growth of bedforms occurs. Both global and local bottom patterns are found. In this study particular emphasis is laid on the mechanism governing the growth of a new type of localised bottom pattern. These patterns consist of small bars located near the entrance of the basin, resembling multiple row bars, and are found when advective sediment fluxes prevail over diffusive sediment fluxes. The formation process of these new bedforms is discussed in detail. The results agree well with field data. Comparison of the results with those obtained with a process-based, numerical model shows that, although the idealised model is strongly simplified, it is capable of producing the essential morphodynamics. Therefore, the idealised model is a useful tool to investigate mechanisms of bottom pattern growth.Responsible Editor: Iris Grabemann     

Observations of the stability of oscillatory flow above the seabed and of sand ripple formation

The results of two field experiments are described, both of which were carried out at Blackpool Sands, Start Bay. In the first experiment in 1978, observations were made of the near-bed flow, and of the movement of coarse sand on the bed, beneath progressive swell waves in shallow water. In the second experiment in 1980, similar observations were made, but for a bed comprising medium to fine sand, and for a more varied range of wave periods. In addition, a number of observations were made of the formation of ripples on an initially flat sand bed. For the naturally rippled beds, critical conditions for the onset of vortex formation and shedding have been established, and reasonable agreement with previous laboratory results has been found. In particular, it has been shown that vortex formation occurs above the lee slopes of ripples only if the near-bed orbital excursion exceeds the ripple wavelength. Prior to certain experimental runs, the area of the seabed in the vicinity of the bottom rig was flattened by divers, and an (equilibrium) ripple pattern was allowed to develop. The wavelengths of the ripples which formed have been found to be in close agreement with the field results of previous workers. To examine in detail some of the properties of separating flow above a rippled bed, an irrotational standing vortex model is presented.     

Hydromechanics for the formation and development of radial sandbanks (II)

In order to study the tidal current ridges, a three-dimensional numerical model is, for the first time, applied to studying the hydrodynamic circumstance with Houbolt’s spiral assumption in the radial sandbank area. It successfully reveals that the radial sandbanks are molded by to-and-fro tidal current as well as the subtransverse circulation current, and that both contribute to maintaining the interior dynamic balance of the sandbanks. It is also found that the subtransverse circulation current would not always appear in pair within the ridges. These discoveries enrich the theoretical results in hydrodynamics of tidal current ridges.     

A storm event watershed model for surface runoff based on 2D fully dynamic wave equations

The main purpose of this work concerns the development and testing of an overland flow model based on the two‐dimensional fully dynamic shallow water equations. Three key aspects, fundamental to get accurate, efficient and robust computation of surface runoff at basin scale, are discussed by transferring the main findings obtained by the recent research on the topic of dam‐break wave and flood propagation in the context of rainfall–runoff modelling. In particular, attention is focused on the numerical flux and bottom slope source terms computation, on a numerical treatment of friction slope terms and on an algorithm for dealing with wetting/drying fronts. The performances of the numerical model have been preliminarily evaluated using experimental or ideal tests characterized by very critical conditions for the stability of a numerical model. Then, attention was focused on a real event occurred in a sub‐basin of Reno river in Italy to analyse the suitability of the model in simulating real flood situations. The numerical results highlight the good performances of the model in all the simulations discussed in the paper. Copyright © 2012 John Wiley & Sons, Ltd.     

表层沉积物特性对地震地面运动的影响研究

建立包含震源、沉积盆地和表层低速沉积层的二维模型,采用交错网格有限差分/伪谱混合方法求解地震波传播,讨论沉积层厚度和速度对地震地面运动的作用。结果表明:沉积层内产生的地震波的多重反射以及转换会引起地面运动持续时间的延长,它们的相干叠加会造成地面运动峰值的放大;随着沉积层速度的增加,多重反射与转换波的能量减小,地面运动持续时间减小,但是不同速度或者不同厚度的低速层模型均显示出一致的地面运动峰值放大特征。结果说明,在包含震源、沉积盆地和沉积层的模型中,沉积层对地面运动的作用机理更复杂。在实际应用中有必要同时考虑这些因素的综合作用。     

Effects of habitat structural complexity on diversity patterns of neotropical fish assemblages in the Bita River Basin,Colombia

Several studies have shown that fish assemblages are structured by habitat features, most of them have proposed that there is a positive relationship between habitat structural complexity and species diversity. In this study, we aimed to test this positive-relationship idea in three habitats types (creeks, oxbow lakes and river sandbanks) distributed along the Bita River Basin in South America. Standardized surveys were conducted during January and February of 2016 (low water period) in 30 sites distributed along the entire basin. We recorded 23,092 individuals representing 191 species. To investigate possible relationships between habitat structural complexity and species diversity, we calculated the first three Hill’s numbers, and performed a Non-metric Multidimensional Scaling (NMDS), a Principal Component Analysis (PCA) and a Canonical Correspondence Analysis (CCA). Our results showed that river sandbanks and creeks had the highest species richness. Results from the NMDS analysis (stress = 0.19) showed that fish community composition was different in the assessed habitats (ANOSIM < p = 0.001). According to the results of the principal component analysis, sand percentage, dissolved oxygen, and vegetation width separated river sandbanks from the other habitats. Results from the Hill’s numbers, forward selection procedure, and canonical correspondence analysis suggested that species composition and diversity were significantly influenced by the habitat structural complexity index and conductivity.