Tidal currents,energy flux and bottom boundary layer thickness in the Clyde Sea and North Channel of the Irish Sea

A high-resolution three-dimensional model of the Clyde Sea and the adjacent North Channel of the Irish Sea is used to compute the major diurnal and semidiurnal tides in the region, the associated energy fluxes and thickness of the bottom boundary layer. Initially, the accuracy of the model is assessed by performing a detailed comparison of computed tidal elevations and currents in the region, against an extensive database that exists for the M₂, S₂, N₂, K₁ and O₁ tides. Subsequently, the model is used to compute the tidal energy flux vectors in the region. These show that the major energy flux is confined to the North Channel region, with little energy flux into the Clyde Sea. Comparison with the observed energy flux in the North Channel shows that its across-channel distribution and its magnitude are particularly sensitive to the phase difference between elevation and current. Consequently, small changes in the computed values of these parameters due to slight changes of the order of the uncertainty in the open-boundary values to the model, can significantly influence the computed energy flux. The thickness of the bottom boundary layer in the region is computed using a number of formulations. Depending upon the definition adopted, the empirical coefficient C used to determine its thickness varies over the range 0.1 to 0.3, in good agreement with values found in the literature. In the North Channel, the boundary layer thickness occupies the whole water depth, and hence tidal turbulence produced at the sea bed keeps the region well mixed. In the Clyde Sea, the boundary layer thickness is a small fraction of the depth, and hence the region stratifies.Responsible Editor: Phil Dyke     

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.     

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.     

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.     

Seasonal variation of the <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript> tide

The seasonal cycle of the main lunar tidal constituent M ₂ is studied globally by an analysis of a high-resolution ocean circulation and tide model (STORMTIDE) simulation, of 19 years of satellite altimeter data, and of multiyear tide-gauge records. The barotropic seasonal tidal variability is dominant in coastal and polar regions with relative changes of the tidal amplitude of 5–10 %. A comparison with the observations shows that the ocean circulation and tide model captures the seasonal pattern of the M ₂ tide reasonably well. There are two main processes leading to the seasonal variability in the barotropic tide: First, seasonal changes in stratification on the continental shelf affect the vertical profile of eddy viscosity and, in turn, the vertical current profile. Second, the frictional effect between sea-ice and the surface ocean layer leads to seasonally varying tidal transport. We estimate from the model simulation that the M ₂ tidal energy dissipation at the sea surface varies seasonally in the Arctic (ocean regions north of 60°N) between 2 and 34 GW, whereas in the Southern Ocean, it varies between 0.5 and 2 GW. The M ₂ internal tide is mainly affected by stratification, and the induced modified phase speed of the internal waves leads to amplitude differences in the surface tide signal of 0.005–0.0150 m. The seasonal signals of the M ₂ surface tide are large compared to the accuracy demands of satellite altimetry and gravity observations and emphasize the importance to consider seasonal tidal variability in the correction processes of satellite data.     

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     

Sensitivity of tidal characteristics in double inlet systems to momentum dissipation on tidal flats: a perturbation analysis

In a tidal channel with adjacent tidal flats, along–channel momentum is dissipated on the flats during rising tides. This leads to a sink of along–channel momentum. Using a perturbative method, it is shown that the momentum sink slightly reduces the M₂ amplitude of both the sea surface elevation and current velocity and favours flood dominant tides. These changes in tidal characteristics (phase and amplitude of sea surface elevations and currents) are noticeable if widths of tidal flats are at least of the same order as the channel width, and amplitudes and gradients of along–channel velocity are large. The M₂ amplitudes are reduced because stagnant water flows from the flats into the channel, thereby slowing down the current. The M₄ amplitudes and phases change because the momentum sink acts as an advective term during the fall of the tide, such a term generates flood dominant currents. For a prototype embayment that resembles the Marsdiep–Vlie double–inlet system of the Western Wadden Sea, it is found that for both the sea surface elevation and current velocity, including the momentum sink, lead to a decrease of approximately 2% in M₂ amplitudes and an increase of approximately 25% in M₄ amplitudes. As a result, the net import of coarse sediment is increased by approximately 35%, while the transport of fine sediment is hardly influenced by the momentum sink. For the Marsdiep–Vlie system, the M₂ sea surface amplitude obtained from the idealised model is similar to that computed with a realistic three–dimensional numerical model whilst the comparison with regard to M₄ improves if momentum sink is accounted for.     

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.     

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.     

The oceanic tides in the South Atlantic Ocean

The finite element ocean tide model of Le Provost and Vincent (1986) has been applied to the simulation of the M₂ and K₁ components over the South Atlantic Ocean. The discretisation of the domain, of the order of 200 km over the deep ocean, is refined down to 15 km along the coasts, such refinement enables wave propagation and damping over the continental shelves to be correctly solved. The marine boundary conditions, from Dakar to Natal, through the Drake passage and from South Africa to Antarctica, are deduced from in situ data and from Schwiderski’s solution and then optimised following a procedure previously developed by the authors. The solutions presented are in very good agreement with in situ data: the root mean square deviations from a standard subset of 13 pelagic stations are 1.4 cm for M₂ and 0.45 cm for K₁, which is significantly better overall than solutions published to date in the literature. Zooms of the M₂ solution are presented for the Falkland Archipelago, the Weddell Sea and the Patagonian Shelf. The first zoom allows detailing of the tidal structure around the Falklands and its interpretation in terms of a stationary trapped Kelvin wave system. The second zoom, over the Weddell Sea, reveals for the first time what must be the tidal signal under the permanent ice shelf and gives a solution over that sea which is generally in agreement with observations. The third zoom is over the complex Patagonian Shelf. This zoom illustrates the ability of the model to simulate the tides, even over this area, with a surprising level of realism, following purely hydrodynamic modelling procedures, within a global ocean tide model. Maps of maximum associated tidal currents are also given, as a first illustration of a by-product of these simulations.     

Tide model comparison over the Southwestern Atlantic Shelf

Sea surface height (SSH) as measured by satellites has become a powerful tool for oceanographic and climate related studies. Whereas in the open ocean good accuracy has been achieved, more energetic dynamics and a number of calibration problems have limited applications over continental shelves and near the coast. Tidal ranges in the Southwestern Atlantic (SWA) continental shelf are among the highest in the world ocean, reaching up to 12 m at specific locations. This fact highlights the relevance of the accuracy of the tidal correction that must be applied to the satellite data to be useful in the region. In this work, amplitudes and phases of tidal constituents are extracted from five global tide models and three regional models and compared to the corresponding harmonics estimated from coastal tide gauges (TGs) and satellite altimetry data. The Root Sum Square (RSS) of the misfit of the common set of the five tidal constituents solved by the models (M₂, N₂, S₂, K₁ and O₁) is higher than 18 cm close to the coast for two of the regional models and higher than 24.5 cm for the rest of the models considered. Both values are too high to provide an accurate estimation of geostrophic non-tidal currents from satellite altimetry in the coastal region. On the other hand, the global model with the highest spatial resolution has a RSS lower than 4.5 cm over the continental shelf even when the non-linear M₄ overtide is considered. Comparison with in-situ current measurements suggests that this model can be used to de-tide altimetry data to compute large-scale patterns of SSH and associated geostrophic velocities. It is suggested that a local tide model with very high resolution that assimilates in-situ and satellite data should meet the precision needed to estimate geostrophic velocities at a higher resolution both close to the coast and over the Patagonian shelf.     

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.     

On the sensitivity of computed surges to open-boundary formulation

A coarse-grid (resolution of order 7 km) model of the west coast of Britain is used to examine the sensitivity of computed storm-surge elevations and currents to a range of open-boundary conditions. The storm-surge period 1 to 26 March 1994 is used for this comparison, as it is a time of significant wind activity. Also current measurements in the North Channel of the Irish Sea together with coastal elevation measurements are available for model validation. Elevations and currents previously computed with a coarse-grid shelf-wide model can also be incorporated into the open-boundary condition to examine the influence of far-field effects. Initial model calculations with no far-field input show the importance of including shelf-wide effects from either the external shelf model, or by using observations from coastal gauges interpolated along the open boundary of the west-coast model. Provided the west-coast models open boundary is taken sufficiently far away from the region of interest, in this case the Irish Sea, then either a radiation condition or an elevation-specified condition is appropriate provided far-field effects are taken into account. If these are not included, then neither boundary condition is successful. For the radiation condition it is necessary to include both elevations and currents from a far-field model in order to reproduce the surge. In the case of an elevation-specified boundary condition far-field effects can be incorporated in hindcast calculations by including observed sea-level changes. In a storm-surge prediction calculation the radiation condition with a far-field model is required. Calculations show that computed elevations are spatially more coherent than currents, with flows through the western Irish Sea showing the greatest sensitivity to open-boundary formulation during storm events.Responsible Editor: Phil Dyke     

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

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

Application of a finite element model to the computation of tides in the Mersey Estuary and Eastern Irish Sea

A variable mesh finite element model of the Irish and Celtic Sea regions with/without the inclusion of the Mersey estuary is used to examine the influence of grid resolution and the Mersey upon the higher harmonics of the tide in the region. Comparisons are made with observations and published results from finite difference models of the area. Although including a high resolution representation of the Mersey had little effect upon computed tides in the western Irish Sea it had a significant effect upon tidal currents in the eastern Irish Sea. In addition the higher harmonics of the M₂ tide in near-shore regions of the eastern Irish Sea particularly the Solway and Mersey estuary together with Morecambe Bay showed significant small scale variability. The Mersey was used to test the sensitivity to including estuaries because high resolution accurate topography was available. The results presented here suggest that comparable detailed topographic data sets are required in all estuaries and near-shore regions. In addition comparisons clearly show the need for an unstructured grid model of the region that can include all the estuaries. Such an unstructured grid solution was developed here within a finite element approach, although other methods in particular the finite volume, or coordinate transformations/curvilinear grids and nesting could be applied.     

M<Subscript>2</Subscript> tidal dynamics in Bohai and Yellow Seas: a hybrid data assimilative modeling study

A high-resolution hybrid data assimilative (DA) modeling system is adapted to study the M₂ barotropic tidal characteristics and dynamics in the Bohai and Yellow Seas. In situ data include tidal harmonics extracted from both coastal sea level and bottom pressure observations. The hybrid DA system consists of both forward and inverse models. The former is three-dimensional, finite-difference, nonlinear Regional Ocean Modeling System (ROMS). The latter is a three-dimensional, linearized, frequency-domain, finite-element model TRUXTON. The DA system assimilates in situ observations via the inversion of the barotropic tidal open boundary conditions (OBCs). Model skill is evaluated by comparing misfits between the observed and modeled tidal harmonics. The assimilation scheme is found effective and efficient in correcting the tidal OBCs, which in turn improves ROMS tidal solutions. Up to 50% reduction of model/data misfits is achieved after data assimilation. M₂ co-tidal maps constructed from the posterior (data assimilative) ROMS solutions agree well with observational analysis of (Fang et al. 2004). Detailed analyses on tidal mixing, residual current, energy flux, dissipation, and momentum term balance dynamics are performed for M₂ constituent, revealing complex M₂ tidal characteristics in the study region and the important role of coastal geometry and topography in affecting regional tidal dynamics.     

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

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

     

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.     

A three-dimensional finite-element model of wind effects upon higher harmonics of the internal tide

A non-linear three-dimensional unstructured grid model of the M₂ tide in the shelf edge area off the west coast of Scotland is used to examine the spatial distribution of the M₂ internal tide and its higher harmonics in the region. In addition, the spatial variability of the tidally induced turbulent kinetic energy and associated mixing in the area are considered. Initial calculations involve only tidal forcing, although subsequent calculations are performed with up-welling and down-welling favourable winds to examine how these influence the tidal distribution (particularly the higher harmonics) and mixing in the region. Both short- and long-duration winds are used in these calculations. Tidal calculations show that there is significant small-scale spatial variability particularly in the higher harmonics of the internal tide in the region. In addition, turbulence energy and mixing exhibit appreciable spatial variability in regions of rapidly changing topography, with increased mixing occurring above seamounts. Wind effects significantly change the distribution of the M₂ internal tide and its higher harmonics, with appreciable differences found between up- and down-welling winds and long- and short-duration winds because of differences in mixing and the presence of wind-induced flows. The implications for model validation, particularly in terms of energy transfer to higher harmonics, and mixing are briefly discussed.     

Tidal friction in a sea with two equal semidiurnal tidal constituents

The effect of quadratic friction on tidal currents consisting of equal M₂ and S₂ constituents is considered. It is shown by two separate arguments—one based on an energy balance, the other on harmonic analysis of the frictional force—that, for rectilinear and parallel currents, the drag coefficient applicable to either constituent considered in isolation should be 1.70 times greater than that applied to the two constituents propagating together. The results of a numerical model of the tides in Gulf St Vincent, Australia (where equal M₂ and S₂ tides occur) are consistent with this prediction. A general result of this work is that the drag coefficients predicted by harmonic analysis of the friction force give the correct rate of energy dissipation for any number of tidal constituents, equal or not.