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.     

Density and flow structure in the Clyde Sea front

A well-defined front in temperature and salinity separates the stratified Clyde Sea water from the vertically well mixed water of the North Channel. The detailed structure of the front was observed in autumn 1990 by a combination of, repeated crossings of the front using a ship-borne ADCP and a towed undulating CTD system, and the deployment of a fixed mooring system with temperature, salinity and velocity sensors for a period of 12 days. The results show that the front was situated on the Great Plateau near a contour of log₁₀(H/U³₂)=2.7∼3.7 where H is the water depth and U₂ the amplitude of M₂ tidal velocity. The temperature structure in the Clyde Sea was inverted and the Clyde Sea surface temperature was lower than that of the vertically well mixed water in the North Channel. Since the salinity gradient was stronger than the temperature gradient with fresher water on the surface, the density structure was predominantly controlled by salinity. There were indications of warm and saline bottom water upwelling on the mixed side of the front during spring tides. This upwelling disappeared and the salinity and temperature structure at the front was more diffuse during the neap tide period. A jet-like along-front residual current was observed flowing to the northwest in the surface layer with a counter flow to the southeast in the bottom layer. The vertical difference in velocity was about 9 cm s⁻¹ and was approximately consistent with the shear determined from the thermal wind relation. Both cross- and along-front components of the current observed at the mooring station varied in response to the advection of the front, although both components had large variations with periods of less than one day and several days. The front was advected past the mooring system by a mean flow from the North Channel to the inner basin, while oscillating 3–5 km back and forth with the tidal currents. From the velocity at a current meter mooring and CTD data, the front was estimated to have moved up to 20 km during the observational period and the cross frontal velocity was inferred to be 3–4 cm s⁻¹.     

Modelling tidally induced sediment-transport paths over the northwest European shelf: the influence of sea-level reduction

A three-dimensional model covering the northwest European Shelf and part of the adjacent Atlantic Ocean is used to examine the influence of water depth change upon the distribution of maximum tidal bed stress. The direction of bed stress is an indicator of sediment movement as bed load and various regions of convergence and divergence in good agreement with observations are identified. Calculations are performed with water depths reduced by 35 m, corresponding to 10 000 years before present (B.P.). Initially, the model is forced by only the M₂ tide, although subsequently five constituents, namely M₂, S₂, N₂, K₁ and O_1, are used for tidal forcing. Although the distribution of extreme bed stresses computed with only M₂ tidal forcing is comparable to that computed with five tides, the additional tidal constituents modify the magnitude of the bed stress. In particular the diurnal tides show regions of local enhanced current amplitude in the shelf-edge region with corresponding changes in bed stress. When water depths are reduced such that the North Sea and English Channel are separated, then there is a significant change in the tidal distribution in the shallow Southern Bight which influences bed-stress distributions and hence bed-load sediment transport in the area. Besides changes in shallow regions, the distribution of tides at the shelf edge is affected. A discussion of the limitations of the present coarse-grid model in shelf-edge regions and how it can be used to provide boundary conditions for limited-area three-dimensional models that can include stratification is presented. Also the importance of stratification for sediment movement at the shelf edge is briefly discussed.Responsible Editor: Phil Dyke     

Dispersion of dissolved trace metals from the Irish Sea into Scottish coastal waters

An investigation has been undertaken into the dispersal of contaminants from the Irish Sea into coastal waters of Scotland via the North Channel. A total of 97 surface samples have been analysed for dissolved copper, cadmium and lead. Salinity and reactive phosphate have also been determined. Evidence is presented to suggest that copper, cadmium and reactive phosphate behave essentially conservatively on mixing into Scottish coastal waters. This behaviour is likened to the dispersal of¹³⁷Cs from the Sellafield nuclear fuel reprocessing plant. It is suggested that this simple mechanism is inadequate to account for the lead distribution. It is proposed that this element is partly taken up by suspended particulates and sediments in the well-mixed turbid waters of the North Channel.It has been demonstrated elsewhere that contaminants from the Irish Sea, such as¹³⁷Cs enter the Firth of Clyde from the North Channel. In the present study North Channel waters are demonstrated to be an important source of trace metals to the Firth of Clyde. At the time of this survey however high concentrations of trace metals were not entering the Firth of Clyde from the North Channel. This is principally attributed to a salinity front associated with the entrance of the Firth which hinders transport across the sill.     

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.     

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

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

An inter-comparison of tidal solutions computed with a range of unstructured grid models of the Irish and Celtic Sea Regions

Three finite element codes, namely TELEMAC, ADCIRC and QUODDY, are used to compute the spatial distributions of the M₂, M₄ and M₆ components of the tide in the sea region off the west coast of Britain. This region is chosen because there is an accurate topographic dataset in the area and detailed open boundary M₂ tidal forcing for driving the model. In addition, accurate solutions (based upon comparisons with extensive observations) using uniform grid finite difference models forced with these open boundary data exist for comparison purposes. By using boundary forcing, bottom topography and bottom drag coefficients identical to those used in an earlier finite difference model, there is no danger of comparing finite element solutions for “untuned unoptimised solutions” with those from a “tuned optimised solution”. In addition, by placing the open boundary in all finite element calculations at the same location as that used in a previous finite difference model and using the same M₂ tidal boundary forcing and water depths, a like with like comparison of solutions derived with the various finite element models was possible. In addition, this open boundary was well removed from the shallow water region, namely the eastern Irish Sea where the higher harmonics were generated. Since these are not included in the open boundary, forcing their generation was determined by physical processes within the models. Consequently, an inter-comparison of these higher harmonics generated by the various finite element codes gives some indication of the degree of variability in the solution particularly in coastal regions from one finite element model to another. Initial calculations using high-resolution near-shore topography in the eastern Irish Sea and including “wetting and drying” showed that M₂ tidal amplitudes and phases in the region computed with TELEMAC were in good agreement with observations. The ADCIRC code gave amplitudes about 30 cm lower and phases about 8° higher. For the M₄ tide, in the eastern Irish Sea amplitudes computed with TELEMAC were about 4 cm higher than ADCIRC on average, with phase differences of order 5°. For the M₆ component, amplitudes and phases showed significant small-scale variability in the eastern Irish Sea, and no clear bias between the models could be found. Although setting a minimum water depth of 5 m in the near-shore region, hence removing wetting and drying, reduced the small-scale variability in the models, the differences in M₂ and M₄ tide between models remained. For M₆, a significant reduction in variability occurred in the eastern Irish Sea when a minimum 5-m water depth was specified. In this case, TELEMAC gave amplitudes that were 1 cm higher and phases 30° lower than ADCIRC on average. For QUODDY in the eastern Irish Sea, average M₂ tidal amplitudes were about 10 cm higher and phase 8° higher than those computed with TELEMAC. For M₄, amplitudes were approximately 2 cm higher with phases of order 15° higher in the northern part of the region and 15° lower in the southern part. For M₆ in the north of the region, amplitudes were 2 cm higher and about 2 cm lower in the south. Very rapid M₆ tidal-phase changes occurred in the near-shore regions. The lessons learned from this model inter-comparison study are summarised in the final section of the paper. In addition, the problems of performing a detailed model–model inter-comparison are discussed, as are the enormous difficulties of conducting a true model skill assessment that would require detailed measurements of tidal boundary forcing, near-shore topography and precise knowledge of bed types and bed forms. Such data are at present not available.     

The influence of tides, wind and waves on the net sand transport in the North Sea

Large-scale redistribution of sand by hydrodynamical processes in shelf seas is important for basin and coastal evolution on time scales of a thousand to tens of thousands of years. The influence of tides on the large-scale net sand-transport patterns in the North Sea has received much attention, but the influence of wind-driven flow and wind waves has hardly been investigated. Here, to establish the present-day situation and to develop a method that can also be used for palaeo-situations and forecasts for different sea levels, this influence is assessed for the present southern North Sea using a numerical flow model, a parametric wave model and a wave-averaged sand-transport formulation. Various forcing combinations are used to identify the dominant transport mechanisms: tides only, tides and wind, tides and waves, and combined tides, wind and waves. Wind forcing is applied in two ways to find an efficient, but still representative, method of incorporating this stochastic process: a statistical wind climatology and an observed time series. The results show that (i) the wind climatology yields a good approximation of the sand transport computed using the time series; (ii) wind-driven flow and waves only contribute significantly to the net sand transport by tides when acting together where tidal currents are small; and (iii) various combinations of forcings dominate the net sand transport in different regions of the southern North Sea: (a) tides dominate in the southern, middle and northwestern parts of the Southern Bight and in the region of The Wash; (b) tides, wind-driven flow and waves all are important in the northeastern part of the Southern Bight; and (c) wind-driven flow and waves dominate north of the Friesian Islands, in the German Bight and on the Dogger Bank. Qualitative comparison with observations shows good agreement.     

Modeling studies of tidal dynamics and the associated responses to coastline changes in the Bohai Sea,China

Over the past 30 years, reclamation projects and related changes have impacted the hydrodynamics and sediment transport in the Bohai Sea. Three-dimensional tidal current models of the Bohai Sea and the Yellow Sea were constructed using the MIKE 3 model. We used a refined grid to simulate and analyze the effects of changes in coastline, depth, topography, reclamation, the Yellow River estuary, and coastal erosion on tidal systems, tide levels, tidal currents, residual currents, and tidal fluxes. The simulation results show that the relative change in the amplitude of the half-day tide is greater than that of the full-day tide. The changes in the tidal amplitudes of M₂, S₂, K₁, and O₁ caused by coastline changes accounted for 27.76–99.07% of the overall change in amplitude from 1987 to 2016, and water depth changes accounted for 0.93–72.24% of the overall change. The dominant factor driving coastline changes is reclamation, accounting for 99.55–99.91% of the amplitude changes in tidal waves, followed by coastal erosion, accounting for 0.05–0.40% of the tidal wave amplitude changes. The contribution of changes in the Yellow River estuary to tidal wave amplitude changes is small, accounting for 0.01–0.12% of the amplitude change factor. The change in the highest tide level (HTL) is mainly related to the amplitude change, and the correlation with the phase change is small. The dominant factor responsible for the change in the HTL is the tide amplitude change in M2, followed by S2, whereas the influence of the K1 and O1 tides on the change in the HTL is small. Reclamation resulted in a decrease in the vertical average maximum flow velocity (V_VAM) in the Bohai Sea. Shallower water depths have led to an increase in the V_VAM; deeper water depths have led to a decrease in the maximum flow velocity. The absolute value of the maximum flow velocity gradually decreases from the surface to the bottom, but the relative change value is basically constant. The changes in the tidal dynamics of the Bohai Sea are proportional to the degree of change in the coastline. The maximum and minimum changes in the tidal flux appear in Laizhou Bay (P-LZB) and Liaodong Bay (P-LDB), respectively. The changes in the tidal flux are related to the change in the area of the bay. Due to the reduced tidal flux, the water exchange capacity of the Bohai Sea has decreased, impacting the ecological environment of the Bohai Sea. Strictly controlling the scale of reclamation are important measures for reducing the decline in the water exchange capacity of the Bohai Sea and the deterioration of its ecological environment.     

A model for tides and currents in the English Channel and southern North Sea

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O₁, K₁, M₂, S₂, N₂, K₂, M₄, MS₄, MN₄, M₆, and 2MS₆.     

Changes in the dynamics/energetics of surface and internal tides in the White Sea on the coexistence of shore-fast and drifting ice covers

The results of modeling for _M2${\mathrm{M}}_2$ surface and internal tides in the White Sea are discussed. These results are obtained for the case when shore-fast and drifting ice covers are present concurrently. It is assumed that the interface between ice covers is of non-tidal origin (i.e., it is pre-assigned) and that ice rheology is viscous-elastic, representative of the low temperatures typical of winter conditions. Emphasis is placed on tidal energetics and, in particular, on the averaged (over a tidal cycle) values of the density and the dissipation rate of barotropic/baroclinic tidal energy. It is shown that in the White Sea, unlike in other marginal seas, the averaged (over a tidal cycle) and depth-integrated density of baroclinic tidal energy for the combined ice cover is much less than the same defined density of barotropic tidal energy. Similarly, the averaged and integrated (over the volume of the White Sea) rate of baroclinic tidal energy dissipation is much less than the same defined rate of barotropic tidal energy dissipation. The latter, in turn, is greater than for the shore-fast ice cover, but is smaller than for the drifting ice cover.     

On the generation and propagation of internal solitary waves in the southern Andaman Sea: A numerical study

Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs.     

Seasonal circulation and influence factors of the Bohai Sea: a numerical study based on Lagrangian particle tracking method

Seasonal circulation of the Bohai Sea (BS) in 1992 was investigated using Lagrangian particle tracking method. The hydrography of the BS was simulated based on an unstructured grid, finite-volume, three-dimensional primitive equation ocean model. With the use of the unstructured triangular grid, the model can easily fit the irregular coastal boundary of the BS. The simulated tides, tidal current, and thermohaline field agreed well with the observations. The transport of particles has three-dimensional structure in the BS. Compared with central Bohai and Bohai Strait, the differences of particles’ transportation between surface and bottom layer in three bays are small. The circulation in the summer is stronger than that in the winter, with the average residual velocity in the surface layer being about 3.7 cm/s during the summer while only 1.8 cm/s during the winter. Using the same model, several well-designed numerical experiments were performed to investigate the effect of oceanic tide, river discharge, wind stress, and thermal stratification on the circulation. It is shown that winds play an important role in the circulation of the BS during both the winter and the summer. Density circulation is important during the summer; however, it is negligible during the winter. River runoff only affects the area around the river mouth. Compared with wind and thermohaline effect, the contribution of tides is small during the summer, and the circulation under only M₂ tidal constituent could not reflect the actual circulation of the BS.     

Mechanisms controlling the intra-annual mesoscale variability of SST and SPM in the southern North Sea

Thermal and optical remote sensing data were used to investigate the spatial and temporal distribution of sea surface temperature (SST) and of suspended particulate matter (SPM) in the southern North Sea. Monthly SST composites showed pronounced seasonal warming of the southern North Sea and delineated the English coastal and continental coastal waters. The East-Anglia Plume is the dominant feature of the English coastal waters in the winter and autumn SPM composites, and the Rhine region of freshwater influence (ROFI), including the Flemish Banks, is the dominant feature of the continental waters. These mesoscale spatial structures are also influenced by the evolution of fronts, such as the seasonal front separating well-mixed water in the southern Bight, from the seasonally stratified central North Sea waters. A harmonic analysis of the SST and SPM images showed pronounced seasonal variability, as well as spring-neap variations in the level of tidal mixing in the East Anglia Plume, the Rhine ROFI and central North Sea. The harmonic analysis indicates the important role played by the local meteorology and tides in governing the SST and near-surface SPM concentrations in the southern North Sea. In the summer, thermal stratification affects the visibility of SPM to satellite sensors in the waters to the north of the Flamborough and Frisian Fronts. Haline stratification plays an important role in the visibility of SPM in the Rhine ROFI throughout the year. When stratified, both regions typically exhibit low surface SPM values. A numerical model study, together with the harmonic analysis, highlights the importance of tides and waves in controlling the stratification in the southern North Sea and hence the visibility of SPM.     

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M₂ tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.     

High-frequency loading effects by the Ligurian Sea — a statistical investigation

In the present work we analyzed the high-frequency band of crustal tilts at Genoa in order to investigate indirect loading effects by the quarter-diurnal oceanic tides, as well as by an observed oceanic oscillation of 3.66 h which was previously ascribed to the proper oscillation of the Ligurian Sea. With this aim two hourly series of tidal observation recorded by an horizontal pendulum along a NS direction have been submitted to spectral analyses (1 May 1965-28 February 1966; 1 June 1966-31 December 1966).Power spectra revealed two peaks near the periods of 6.15 and 3.66 h and highly resolved Fourier spectra allowed us to detect the loading effects by the oceanic tides M₄, MS₄ and MK₄. As regards to the oscillation of 3.66 h we have found a spreading of spectral lines and non-significant values for the phases. This result provides a decisive verification of the existence of a proper oscillation of the Ligurian Sea regarded as a wide oscillating system with an open boundary from Nice (Côte d'Azur) to Calvi (Corsica).Finally, a spectral analysis performed on sea-level observations at Genoa revealed a complete correspondence between ocean and earth oscillations in the quarter-diurnal band and at the frequency of the longitudinal free oscillation of the Ligurian basin, with a mean amplitude ratio of about 1 mseca/mm.     

An idealized model of tidal dynamics in the North Sea: resonance properties and response to large-scale changes

An idealized process-based model is developed to investigate tidal dynamics in the North Sea. The model geometry consists of a sequence of different rectangular compartments of uniform depth, thus, accounting for width and depth variations in a stepwise manner. This schematization allows for a quick and transparent solution procedure. The solution, forced by incoming Kelvin waves at the open boundaries and satisfying the linear shallow water equations on the f plane with 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. First, the general resonance properties of a strongly simplified geometry with two compartments, representing the Northern North Sea and Southern Bight, are studied. Varying the forcing frequency while neglecting bottom friction reveals Kelvin and Poincaré resonance. These resonances continue to exist (but with lower amplification and a modified spatial structure) when adding the Dover Strait as a third compartment and separating the solutions due to forcing from either the north or the south only. Including bottom friction dampens the peaks. Next, comparison with tide observations along the North Sea coast shows remarkable agreement for both semi-diurnal and diurnal tides. This result is achieved with a more detailed geometry consisting of 12 compartments fitted to the coastline of the North Sea. Further simulations emphasize the importance of Dover Strait and bottom friction. Finally, it is found that a sea level rise of 1 m, uniformly applied to the entire North Sea, amplifies the M2-elevation amplitudes almost everywhere along the coast, with an increase of up to 8 cm in Dover Strait. Bed level changes of ±1 m, uniformly applied to the Southern Bight only, imply weaker changes, with changes in coastal M2-elevation amplitudes below 5 cm.     

On the circulation in the East Frisian Wadden Sea: numerical modeling and data analysis

 In this paper we use a combination of numerical modeling and data analysis to gain a better understanding of the major characteristics of the circulation in the East Frisian Wadden Sea. In particular, we concentrate on the asymmetry of the tidal wave and its modulation in the coastal area, which results in a complex pattern of responses to the sea-level forcing from the North Sea. The numerical simulations are based on the 3-D primitive equation General Estuarine Transport Model (GETM) with a horizontal resolution of 200 m and terrain-following vertical coordinates. The model is forced at its open boundaries with sea-level data from an operational model for the German Bight (German Hydrographic Office). The validation data for our model simulations include time series of tidal gauge data and surface currents measured at a pile in the back-barrier basin of the Island Langeoog, as well as several ADCP transects in the Accumer Ee tidal inlet. Circulation and turbulence characteristics are investigated for typical situations driven by spring and neap tides, and the analysis is focused on dominating temporal and spatial patterns. By investigating the response of five back-barrier basins with rather different morphologies to external forcing, an attempt is made to elucidate the dominating physical balances controlling the circulation in the individual sub-basins. It is demonstrated that the friction at the seabed tends to slow down the tidal signal in the shallow water. This leads to the establishment of flood dominance in the shallow sea north of the barrier islands. South of the islands, where the water volume of the channels at low tide is smaller than the tidal prism, the asymmetry of the tidal signal is shifted towards ebb dominance, a feature which is particularly pronounced at spring tide. At the northern open boundary, the tidal wave propagating from west to east generates a sea-level difference of ∼1 m along the boundary, and thereby triggers vigorous alongshore currents. The frictional control in the model is located in the inlets, as well as along the northern boundary. The correlation between velocity and turbulent kinetic energy tends to the establishment of a net southward transport, giving theoretical support to the observed accumulation of sediments on the intertidal flats. Weak turbulence along the northern shores of the barrier islands and the small magnitude of the residual currents there promote accumulation of suspended matter in these areas, although wave action will generally counteract this effect. Received: 29 May 2002 / Accepted: 26 September 2002 Responsible Editor: Jean-Marie Beckers Acknowledgements We are indebted to S. Dick for providing the data from the operational model of BSH and to B. Flemming for the useful discussions. The topography data and Fig. 1 have been prepared in cooperation with F. Meyer. Figure 2 has been prepared by G. Brink-Spalink. We also thank for the comments from an anonymous reviewer which helped to improve our paper.     

Tides and mixing in the northwestern East China Sea Part I: Rotating and reversing tidal flows

Bottom-mounted ADV and ADCP instruments in combination with CTD profiling measurements taken along the Chinese coast of the East China Sea were used to study the vertical structure of temperature, salinity, and velocity in reversing tidal currents on a shallow inner shelf and in rotating tidal flows over a deeper sloping bottom of the outer shelf. These two regimes of barotropic tide affect small-scale dynamics in the lower part of the water column differently. The reversing flow was superimposed by seiches of ∼2.3 h period generated in semienclosed Jiaozhou Bay located nearby. As the tidal vector rotates over the sloping bottom, the height of the near-bottom logarithmic layer is subjected to tidal-induced variations. A maximum of horizontal velocity U_max appears at the upper boundary of the log layer during the first half of the current vector rotation from the minor to the major axis of tidal ellipse. In rotating tidal flow, vertical shear generated at the seafloor, propagated slowly to the water interior up to the height of U_max, with a phase speed of ∼5 m/h. The time-shifted shear inside the water column, relative to the shear at the bottom, was associated with periodically changing increases and decreases of the tidal velocity above the log layer toward the sea surface. In reversing flows, the shear generated near the bottom and the shear at the upper levels were almost in phase.