Ocean tides and resonance

Tidal currents and surface amplitudes are calculated globally for the dominating diurnal and semidiurnal constituents using an established tidal model under a range of altered bathymetry. The purpose is to evaluate if the well-known amplification of the global tides during the Last Glacial Maximum (LGM) is related to changed propagation properties for the tidal wave or to changed damping due to removal of shelf seas. The response of the tides and tidal dissipation to future sea-level rise is also discussed. The tides in the present and LGM oceans were simulated first, followed by runs where the present day bathymetry was used but the shelf seas removed by the introduction of vertical walls or where sea level is allowed to rise. Previously reported results regarding tidal amplitudes and dissipation rates are reproduced in the control runs. The runs without shelf seas show significantly enhanced tidal amplitudes in the North Atlantic, whereas sea-level rise of 5 m above present levels show a significant shift in the amphidromic points on a local and regional scale but had a limited effect on the open ocean tides. Simulations with very large sea-level rise show a significantly decreased global tidal dissipation, whereas experiments without friction in present-day shallow water display results similar to those with no shelf seas. The results all point towards changing damping properties due to the removal of shelf seas as being the mechanism behind the LGM amplification, and they imply the importance of implementing future sea-level changes properly in tidal simulations.     

Celtic Sea and Armorican current structure and the vertical distributions of temperature and chlorophyll

Vertical sections of temperature and chlorophyll a across the slopes and shelf of the Celtic Sea in the summer show the characteristic regimes; oceanic, slope, shelf, frontal, and mixed. Increases of surface chlorophyll a are commonly observed along the shelf tidal fronts where the thermocline outcrops at the surface, and also at the shelf-break. The variations in phytoplankton biomass are most readily interpreted in terms of the effects of physical mixing processes due to wind and tide on the availability of inorganic nutrients and light energy. On the shelf, mixing processes, both due to internal waves, inertial currents, and to boundary induced turbulence caused by tidal shear associated with the sea floor, play an important role in determining the observed vertical structures. A numerical model is used to define regions where tidal mixing processes are likely to be relatively important and provides the physical framework for interpreting the temperature and chlorophyll a profiles.     

Coastal and shelf circulation in the vicinity of Camamu Bay (14°S), Eastern Brazilian Shelf

The Camamu Bay (CMB) is located on the narrowest shelf along the South American coastline and close to the formation of two major Western Boundary Currents (WBC), the Brazil/North Brazil Current (BC/NBC). These WBC flow close to the shelf break/slope region and are expected to interact with the shelf currents due to the narrowness of the shelf. The shelf circulation is investigated in terms of current variability based on an original data set covering the 2002-2003 austral summer and the 2003 austral autumn. The Results show that the currents at the shelf are mainly wind driven, experiencing a complete reversal between seasons due to a similar change in the wind field. Currents at the inner-shelf have a polarized nature, with the alongshore velocity mostly driven by forcings at the sub-inertial frequency band and the cross-shore velocity mainly supra-inertially forced, with the tidal currents playing an important role at this direction. The contribution of the forcing mechanisms at the mid-shelf changes between seasons. During the summer, forcings in the two frequency bands are important to drive the currents with a similar contribution of the tidal currents. On the other hand, during the autumn season, the alongshore velocity is mostly driven by sub-inertial forcings and tidally driven currents still remain important in both directions. Moreover, during the autumn when the stratification is weaker, the response of the shelf currents to the wind forcing presents a barotropic signature. The meso-scale processes related to the WBC flowing at the shelf/slope region also affect the circulation within the shelf, which contribute to cause significant current reversals during the autumn season. Currents at the shelf-estuary connection are clearly supra-inertially forced with the tidal currents playing a key role in the generation of the along-channel velocities. The sub-inertial forcings at this location act mainly to drive the weak ebb currents which were highly correlated with both local and remote wind forcing during the summer season.     

Transport over a narrow shelf: Exuma Cays, Bahamas

Current meter and temperature data were collected over a 402-day period from an outer shelf and a tidal channel study site in the Exuma Cays, Bahamas. The shelf width is less than 2 km, and floods and ebbs through a nearby tidal channel extend across the entire shelf and reduce coherence of wind forcing and along-shelf flow. The data are used in perturbation analyses to investigate the across-shelf turbulent transport of heat and momentum over seasonal time scales. Data show a net landward transport of both heat and momentum over the course of the study, but the perturbation products contain distinct seasonal cycles. In fall and winter months, across-shelf heat and momentum fluxes are landward, while during spring and summer months fluxes are seaward. Comparison of shelf-water temperature with the temperature of bank water leaving on the ebb suggests that seasonal cycles of across-shelf heat and momentum in shelf waters are influenced by the seasonal export of relatively warm and cool water from Great Bahama Bank.Responsible Editor: Iris Grabemann     

Tides, sea-level rise and tidal power extraction on the European shelf

An established numerical tidal model has been used to investigate the impact of various sea-level rise (SLR) scenarios, as well as SLR in combination with large-scale tidal power plants on European shelf tidal dynamics. Even moderate and realistic levels of future SLR are shown to have significant impacts on the tidal dynamics of the area. These changes are further enhanced when SLR and tidal power plants are considered in combination, resulting in changes to tidal amplitudes, currents and associated tidal dissipation and bed shear stresses. Sea-level rise is the dominant influence on any far-field impacts, whereas tidal power plants are shown to have the prevailing influence over any changes close to the point of energy extraction. The spatial extent of the impacts of energy extraction is shown to be affected by the sea level when more than one tidal power plant in the Irish Sea was considered. Different ways to implement SLR in the model are also discussed and shown to be of great significance for the response of the tides.     

Tidal ice drift and ice-generated changes in the tidal dynamics/energetics on the Siberian continental shelf

Tidal ice drift is regarded as an element of the 3D tidal dynamics on the Siberian continental shelf. Two cases are considered: (1) when sea ice is immobile (in a horizontal plane), so that ice-induced changes of tidal characteristics may be treated as if they are limiting, and (2) when sea ice is moveable and internal stresses in the ice cover are described by a viscous-elastic rheology. It is shown that sea ice does not lead to radical changes of the tidal and energetic regimes, although their quantitative changes may be quite significant. In general, the ice-induced influence on the tidal dynamics is less than that on the tidal energetics. Therefore, the commonly accepted assumption that this influence may be viewed as being negligible is justified only partially. We present model results for tidal ice drift parameters—its magnitude, direction, the amplitude of tidal variations of ice concentration and the pressure of ice compression—as well as for ice-induced changes of tidal characteristics and the residual tidal ice drift. Partial attention is given to revealing the zones of ice compression–rarefaction, that is of importance in Arctic navigation.     

Ice-induced seasonal variability of tidal constants in the Arctic Ocean

The results for three-dimensional (3D) winter and summer tidal flows in the homogeneous Arctic Ocean, obtained with the use of a modified version of the 3D finite-element hydrothermodynamic model QUODDY-4, are presented. It is shown that seasonal variability of the M₂ tidal constants (amplitudes and phases of tidal sea surface level elevations) in the Central and Canadian parts of the Arctic Ocean is less than the error in the predicted tidal sea surface level elevations. This means that the seasonal variability can be neglected at least as a first approximation. A different situation is encountered in the Siberian continental shelf, where seasonal changes of tidal amplitude are ±5 cm, while those of tidal phase vary from 15° to several tens of degrees.     

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 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.     

Effect of stratification on tidal circulation over the Scotian Shelf and Gulf of St. Lawrence: a numerical study using a three-dimensional shelf circulation model

A three-dimensional shelf circulation model is used to examine the effect of seasonal changes in water-column stratification on the tidal circulation over the Scotian Shelf and Gulf of St. Lawrence. The model is driven by tidal forcing specified at the model’s lateral open boundaries in terms of tidal sea surface elevations and depth-averaged currents for five major tidal constituents (M₂, N₂, S₂, K₁, and O₁). Three numerical experiments are conducted to determine the influence of baroclinic pressure gradients and changes in vertical mixing, both associated with stratification, on the seasonal variation of tidal circulation over the study region. The model is initialized with climatological hydrographic fields and integrated for 16 months in each experiment. Model results from the last 12 months are analyzed to determine the dominant semidiurnal and diurnal tidal components, M₂ and K₁. Model results suggest that the seasonal variation in the water-column stratification affects the M₂ tidal circulation most strongly over the shelf break and over the deep waters off the Scotian Shelf (through the development of baroclinic pressure gradients) and along Northumberland Strait in the Gulf of St. Lawrence (through changes in vertical mixing and bottom stress). For the K₁ constituent, the baroclinic pressure gradient and vertical mixing have opposing effects on the tidal circulation over several areas of the study region, while near the bottom, vertical mixing appears to play only a small role in the tidal circulation.     

Numerical model studies on the generation and dissipation of the diurnal coastal-trapped waves over the Sakhalin shelf in the Sea of Okhotsk

To clarify the generation and dissipation mechanisms of diurnal coastal-trapped waves (CTWs) over the Sakhalin shelf, a series of numerical experiments were conducted using a three-dimensional tidal model of the Okhotsk Sea with density stratification. The tidal model used has good reproduction owing to the careful fitting to the recent observations. The numerical experiments suggested that diurnal CTWs are primarily (~60%) generated by the conversion of tidal energy at the northern corner of the Sakhalin shelf, and further amplified by vorticity generation due to the water column oscillation from Sakhalin Bay and the influence of Kashevarov Bank. From the observations, it was found that diurnal CTWs are effectively dissipated by the strong spin-down due to bottom friction. The conventional turbulent closure model cannot reproduce the observed damping of diurnal CTWs, which raises a caution in modeling the tidal fields in high-latitude regions where diurnal CTWs exist. To resolve this underestimation of the damping, the vertical eddy viscosity was parameterized using its dependence on the observed major axis length of the diurnal tidal current ellipses, which improves the model reproduction on the damping of diurnal CTWs. The model also suggests that the spin-down effects due to friction associated with the sea-ice cover play an important role in the tidal current reduction in the region where diurnal CTWs exist, as the observations suggested.     

Lateral tidal mixing in the Antarctic marginal seas

Tidal mixing plays an important role in the modification of dense water masses around the Antarctic continent. In addition to the vertical (diapycnal) mixing in the near-bottom layers, lateral mixing can also be of relevance in some areas. A numerical tide simulation shows that lateral tidal mixing is not uniformly distributed along the shelf break. In particular, strong mixing occurs all along the Ross Sea and Southern Weddell Sea shelf breaks, while other regions (e.g., the western Weddell Sea) are relatively quiet. The latter regions correspond surprisingly well to areas where indications for cross-shelf exchange of dense water masses have been found. The results suggest that lateral tidal mixing may account for the relatively small contribution of Ross Sea dense water masses to Antarctic Bottom Water.     

Evolution of bed shear stress distribution over the northwest European shelf seas during the last 12,000 years

Due to changes in relative sea level of order 100 m, the contribution of tides and waves to net bed shear stress in shelf sea regions has varied considerably over the Late Glacial and Holocene. Understanding the spatial and temporal distribution of this ratio leads to a deeper understanding of the erosion and deposition of sediments over the shelf seas throughout this time period. Tidal and wave models are here applied to palaeo time slices of the northwest European shelf seas over the last 12,000 years. The model simulations include a series of sensitivity tests to account for the influence of interannual variability in wind conditions on the resulting bed shear stress. The results show that there has been a significant decrease over the last 12,000 years in shelf-scale mobilisation of coarse sediment. Since there was a lower magnitude of wave orbital velocity penetrating to the sea bed as a result of increasing relative sea level, this reduction in sediment mobilisation was primarily controlled by a shelf-scale decrease in wave-induced bed shear stress over the last 12,000 years. The predictions of mean and residual bed shear stress for the modelled palaeo time slices are a useful tool with which to inform site-selection and subsequent interpretation of sediment cores. In addition, the modelled reconstructions of palaeo tidal range over the shelf seas demonstrates the potential errors associated with assuming a present-day tidal range when correcting palaeo sea-level proxies from their deposited datum (e.g. palaeo mean high water spring tide) to palaeo mean sea level.     

Unstructured,anisotropic mesh generation for the Northwestern European continental shelf,the continental slope and the neighbouring ocean

A new mesh refinement strategy for generating high quality unstructured meshes of the Northwestern European continental shelf, the continental slope and the neighbouring ocean is presented. Our objective is to demonstrate the ability of anisotropic unstructured meshes to adequately address the challenge of simulating the hydrodynamics occurring in these three regions within a unique mesh. The refinement criteria blend several hydrodynamic considerations as the tidal wave propagation on the continental shelf and the hydrostatic consistency condition in steep areas. Several meshes illustrate both the validity and the efficiency of the refinement strategy. The selection of the refinement parameters is discussed. Finally, an attempt is made to take into account tidal ellipses, providing another cause for anisotropy in the mesh.     

Numerical study of three-dimensional shelf circulation on the Scotian Shelf using a shelf circulation model

A numerical shelf circulation model was developed for the Scotian Shelf, using a nested-grid setup consisting of a three-dimensional baroclinic inner model embedded inside a two-dimensional barotropic outer model. The shelf circulation model is based on the Princeton Ocean Model and driven by three-hourly atmospheric forcing provided by a numerical weather forecast model and by tidal forcing specified at the inner model's open boundaries based on pre-calculated tidal harmonic constants. The outer model simulates the depth-mean circulation forced by wind and atmospheric pressure fields over the northwest Atlantic Ocean with a horizontal resolution of 1/12°. The inner model simulates the three-dimensional circulation over the Gulf of St. Lawrence, the Scotian Shelf, and the adjacent slope with a horizontal resolution of 1/16°. The performance of the shelf circulation model is assessed by comparing model results with oceanographic observations made along the Atlantic coast of Nova Scotia and in the vicinity of Sable Island (on the Scotian Shelf) during two periods: October 2000–March 2001 and April–June 2002. Analysis of model results on Sable Island Bank indicates that tidal currents account for as much as ∼80% of the total variance of near-bottom currents, and currents driven by local winds account for ∼30% of the variance of the non-tidal near-bottom currents. Shelf waves generated remotely by winds and propagating into the region also play an important role in the near-bottom circulation on the bank.     

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     

Cross-shelf transport into nearshore waters due to shoaling internal tides in San Pedro Bay, CA

In the summer of 2001, a coastal ocean measurement program in the southeastern portion of San Pedro Bay, CA, was designed and carried out. One aim of the program was to determine the strength and effectiveness of local cross-shelf transport processes. A particular objective was to assess the ability of semidiurnal internal tidal currents to move suspended material a net distance across the shelf. Hence, a dense array of moorings was deployed across the shelf to monitor the transport patterns associated with fluctuations in currents, temperature and salinity. An associated hydrographic program periodically monitored synoptic changes in the spatial patterns of temperature, salinity, nutrients and bacteria. This set of measurements show that a series of energetic internal tides can, but do not always, transport subthermocline water, dissolved and suspended material from the middle of the shelf into the surfzone. Effective cross-shelf transport occurs only when (1) internal tides at the shelf break are strong and (2) subtidal currents flow strongly downcoast. The subtidal downcoast flow causes isotherms to tilt upward toward the coast, which allows energetic, nonlinear internal tidal currents to carry subthermocline waters into the surfzone. During these events, which may last for several days, the transported water remains in the surfzone until the internal tidal current pulses and/or the downcoast subtidal currents disappear. This nonlinear internal tide cross-shelf transport process was capable of carrying water and the associated suspended or dissolved material from the mid-shelf into the surfzone, but there were no observation of transport from the shelf break into the surfzone. Dissolved nutrients and suspended particulates (such as phytoplankton) transported from the mid-shelf into the nearshore region by nonlinear internal tides may contribute to nearshore algal blooms, including harmful algal blooms that occur off local beaches.     

Internal tide modelling and the influence of wind effects

Initially the development of shallow sea three-dimensional barotropic tidal models is briefly reviewed with a view to determining what were the key measurements that allowed progress in this field and rigorous model validation. Subsequently this is extended to a brief review of baroclinic tidal models to try to determine a “way forward” for baroclinic model development. The difficulty of high spatial variability, and wind influence are identified as possibly important issues that must be considered in validating baroclinic tidal models. These are examined using a three-dimensional unstructured grid model of the M₂ internal tide on the shelf edge region off the west coast of Scotland. The model is used to investigate the spatial variability of the M₂ internal tide, and associated turbulence energy and mixing in the region. Initial calculations are performed with tidal forcing only, with subsequent calculations briefly examining how the tidal distribution is modified by down-welling and up-welling favourable winds. Calculations with tidal forcing only, show that there is significant spatial variability in the internal tide and associated mixing in the region. In addition, these are influenced by wind effects which may have to be taken into account in any model validation exercise. The paper ends by discussing the comprehensive nature of data sets that need to be collected to validate internal tidal models to the same level currently attained with three dimensional barotropic tidal models.     

Sedimentary indicators of water movement in the western approaches to the English Channel

The continental shelf to the southwest of the British Isles is an area of intense tidal current activity. Although most of the sediment is coarse, it still contains a small proportion of fine (<63 μm) material, consisting mainly of biogenic debris. Coccoliths in particular are both common and widespread and they are found in the adjacent slope sediments. The results presented here show that coccolithophorid diversity is high in the deeper parts of Whittard Canyon, the abyssal plain, and on a small area of shelf. Diversity decreases away from the ocean towards the land. Coccoliths and coccospheres have also been recorded from surface water samples. Apart from the landward movement of oceanic water shown by the coccolithophorids, movement of material on the bottom from shelf to slope is shown by the distribution of benthic diatom frustules and mollusc shell chips cut by clionid sponges. Thus, a study of the fine sediment reveals details of sediment transport and water movement.     

Revising the paradigm of tidal analysis – the uses of non-stationary data

Surface elevation and current records contain non-tidal variance, often dismissed as noise. The processes responsible for the non-tidal component may also modulate the tidal signal, altering its strength and frequency structure. Because of their manner of generation and propagation, internal tides are inherently irregular. The non-stationary character of these and other tidal processes provides an integral and useful property of tidal records, because it provides an opportunity to obtain insights into tidal dynamics and the interaction of tidal and non-tidal processes. It is, moreover, productive to use multiple approaches in analyzing coastal and estuarine tidal processes so that both the time-varying and average frequency content are determined. Only by confronting the causes of non-stationary behaviour in this way can some of the remaining challenges in tidal analysis and prediction be overcome, e.g. shelf and estuarine currents, river tides, internal tides, tide-surge interactions and tidally influenced ecological processes. Several examples illustrate the utility of non-stationary tidal analysis methods.Responsible Editor: Jens Kappenberg