Tidal Energy Budget Research Articles

Impact of sea level rise on tidal energy budget in a macro-tidal coastal bay with archipelago

With sea level rise (SLR), tidal nuisance flooding has become a growing threat, especially around estuaries with large tidal amplitudes. This study investigated how sea level change affects tides in Hangzhou Bay, a macro-tidal estuary with high SLR rate. By downscaling climate projections to a regional hydrodynamic model, the amplitude of primary tidal constituent (M2) was predicted to increase by 0.25 m in the upper bay, where the amplitude of major diurnal tide (K1) was also predicted to increase by 15%. In addition, the sensitivity of tidal amplitude to mean sea level was examined by a set of numerical simulations with different SLR. It was found that the increase of tidal amplitude is nonlinear to SLR, and the tidal amplitudes almost cease to increase when SLR is over 1.5 m. Although predictions show less amplitude changes in the lower bay, Zhoushan Archipelago around the bay mouth strongly modulates the incoming tidal energy, thus affecting the tidal amplitude in the upper bay. Energy budget analysis revealed that the complex topography, such as narrow channels, in the archipelago area leads to strong horizontal shear, which dissipates approximately 25% of total tidal energy in the bay. On the other hand, around 60% of the energy is dissipated in the bottom boundary layer. However, the bottom dissipation decreases by 4% due to reduced friction, while horizontal dissipation increases by 10% due to enhanced horizontal shear with SLR. This suggests that the strong horizontal shear in the Zhoushan archipelago region can play a more important role in the tidal energy budget in the future.

High-Resolving modeling of the surface semidiurnal M<sub>2</sub> tide in the East-Siberian Sea

In the framework of a high-resolving version of the 3D finite-element hydrostatic model QUODDY-4 we have simulated the fields of dynamic characteristics (amplitudes and phases of tidal elevations and barotropic tidal velocity ellipses) corresponding to the surface semidiurnal M2 tide in the no-ice East-Siberian Sea. It is shown that the obtained tidal chart has a complex structure, determined by 4 real amphidromes of left rotation which are induced by interference of counter-coming progressive Poincare waves in the southern part of the sea, 1 fake amphidrome with the center upon the Novaya Sibir Isl. and 4 small-scale amphidromes caused by interference of counter-coming Kelvin waves, from which 3 are formed in the narrow straits in the region of Bolshoy and Maly Lyahovsky Isls. and 1 near the entrance of the Chaunskaya Guba. Tidal amplitudes in the vicinity of the Novaya Sibir Isl. achieve 20–30 cm, whereas in the remaining part of the sea they are comparatively small and do not exceed 5–10 cm. Accordingly, the field of barotropic tidal velocities in the north-western part of the sea basically consists of high values (they are tens of cm/s), but in the other parts of the sea barotropic velocities are small (lower then 10 cm/s) and their field has a band structure. The fields of the averaged (over a tidal cycle) integrated in depth constituents of the barotropic tidal energy budget (namely, the barotropic tidal energy density, the advective transport and the horizontal wave flux per unit length of this energy and the rate of its dissipation due to the bottom friction) are presented. Also, a comparison of predicted tidal elevations with the mareographic level measurement data states that an estimate of their agreement may be considered as satisfactory taking into account that the tidal amplitudes in the sea as a whole are small.

Modulation of Internal Tides by Turbulent Mixing in the South China Sea

Modulations of internal tides (ITs) including the baroclinic tidal energy budget, the incoherency, and the nonlinear interactions among different tidal components by turbulent mixing in the South China Sea (SCS) are investigated through numerical simulations. The baroclinic tidal energy budget can hardly be affected by the structure of mixing. Meanwhile, change in the mixing intensity in a reasonable range also cannot obviously modulate the baroclinic tidal energy budget in the SCS. Compared to the baroclinic energy budget, the distributions of conversion and dissipation are more sensitive to the change of mixing. Turbulent mixing also modulates the incoherency of ITs by changing the horizontal density in the ocean. The horizontal variation of density adds incoherence to ITs largely by affecting the internal tidal amplitudes. Furthermore, nonlinear interactions among different components of ITs are generally modulated by the mixing intensity, whereas the variation of the mixing structure can hardly influence the nonlinear interactions. Therefore, the diapycnal diffusivity can set to be horizontally and vertically homogeneous in most of the internal tidal simulations, except for those in which the incoherency of ITs needs to be simulated. However, excessive strong mixing will destroy the stratification. Thus, the optimum range for IT simulations in the SCS is from O (10–5) to O (10–3) m2s–1.

High-Resolution Modeling of Semidiurnal Internal Tidal Waves in the Laptev Sea in the Ice-Free Period: Their Dynamics and Energetics

The QUODDY-4 three-dimensional finite-element hydrostatic model has been used to reproduce the spatial distributions of dynamic and energetic characteristics of the internal tidal waves (ITWs) of the Laptev Sea in the ice-free period. It has been shown that one distinctive feature of ITW amplitudes at the pycnocline depth is that the area with relatively high ITW amplitudes is limited. The peak amplitudes reaching at least 5 m have been detected only in the central part of the sea near the continental slope, but the ITW amplitudes in the western and eastern parts of the sea do not exceed 0.2 and 0.1 m, respectively. Like ITW amplitudes, the baroclinic tidal velocities are expressed mainly in the central part of the sea and almost vanish in its western and eastern parts. The presence of a zone of high baroclinic velocities near the northern open border of the sea and an increase in velocities with approaching the coast of the continent at the mouth of the Lena River is noted. The fields of components of the averaged (over a tidal cycle) baroclinic tidal energy budget (integrated by depth) are discussed. The averaged (over the sea area) values of the density of baroclinic tidal energy, as well as the tidal energy conversion and dissipation rates, are $$1.2\,\, \times \,\,{{10}^{3}}$$ J/m2, $$ - 0.3\,\, \times \,\,{{10}^{{ - 3}}}$$ W/m2, and $$7.3\,\, \times \,\,{{10}^{{ - 3}}}$$ W/m2, respectively. The ITW lifetime in the Laptev Sea, defined as the ratio of the average density of baroclinic tidal energy to the dissipation rate, is around 50 h; i.e., the ITW lifetime in the sea is 4 times higher than the tidal cycle length for the M2 tidal harmonic.

Revisiting the tidal dynamics in the complex Zhoushan Archipelago waters: A numerical experiment

A complex archipelago exhibits high velocity shear, strong advection, and significant nonlinearity for tides, overtides, tidal currents, and subtidal hydrodynamics. Here, a high-resolution regional ocean modeling system with two-way nesting is applied to the coastal Zhoushan Archipelago in the East China Sea. After validation for the M2, S2, K1, and O1 tidal constituents, the spatial structures of tides and tidal currents are presented. The features of these constituents and two significant overtides of M2 (M4 and M6) are discussed. The M2 tide is dominant in the study domain, followed by the S2, K1, and O1 tides in amplitude in that order. Tidal energy budget analysis shows that about 46.4% of the incoming energy is dissipated inside the study area and 67.3% of the dissipated energy is consumed by the bottom friction, while the remainder passes through the study domain. Jetlike flows in the channels are among the most remarkable features. Analysis of momentum balance terms averaged over the flood or ebb period demonstrates that the primary balance near the islands is between the horizontal advection and the pressure gradient force, suggesting a predominant Bernoulli-type motion with strong nonlinearity. However, in the area away from the islands, the horizontal advection becomes less important. The M4 and M6 tides are mainly generated by nonlinear advection, bottom friction plays a minor role, and the interactions between different constituents also have some influence.

The Lifecycle of Semidiurnal Internal Tides over the Northern Mid-Atlantic Ridge

AbstractThe life cycle of semidiurnal internal tides over the Mid-Atlantic Ridge (MAR) sector south of the Azores is investigated using in situ, a high-resolution mooring and microstructure profiler, and satellite data, in combination with a theoretical model of barotropic-to-baroclinic tidal energy conversion. The mooring analysis reveals that the internal tide horizontal energy flux is dominated by mode 1 and that energy density is more distributed among modes 1–10. Most modes are compatible with an interpretation in terms of standing internal tides, suggesting that they result from interactions between waves generated over the MAR. Internal tide energy is thus concentrated above the ridge and is eventually available for local diapycnal mixing, as endorsed by the elevated rates of turbulent energy dissipation ε estimated from microstructure measurements. A spring–neap modulation of energy density on the MAR is found to originate from the remote generation and radiation of strong mode-1 internal tides from the Atlantis-Meteor Seamount Complex. Similar fortnightly variability of a factor of 2 is observed in ε, but this signal’s origin cannot be determined unambiguously. A regional tidal energy budget highlights the significance of high-mode generation, with 81% of the energy lost by the barotropic tide being converted into modes >1 and only 9% into mode 1. This has important implications for the fraction (q) of local dissipation to the total energy conversion, which is regionally estimated to be ~0.5. This result is in stark contrast with the Hawaiian Ridge system, where the radiation of mode-1 internal tides accounts for 30% of the regional energy conversion, and q < 0.25.

Impact of sea level rise on tidal range in Chesapeake and Delaware Bays

AbstractCoastal inundation is affected not only by rising mean sea level but also by changing tides. A numerical model is developed to investigate how sea level rise and coastline changes may impact tides in two coastal‐plain estuaries, Chesapeake Bay and Delaware Bay. Despite their different tidal characteristics, the two estuaries display similar responses to the sea level rise and shoreline management scenarios. When hypothetic sea walls are erected at the present coastline to prevent low‐lying land from flooding, tidal range increases, with greater amplification in the upper part of the two estuaries. When low‐lying land is allowed to become permanently inundated by higher sea level, however, tidal range in both estuaries decreases. Analyses of the tidal energy budget show that the increased dissipation over the shallow water and newly inundated areas compensates for the reduced dissipation in deep water, leading to smaller tidal range. The changes in the tidal range are not proportional to the changes in the mean sea level, indicating a nonlinear tidal response to sea level rise. The ratio of tidal range change to sea level rise varies between −0.05 and 0.1 in Chesapeake Bay and between −0.2 and 0.25 in Delaware Bay. The model results suggest a potential adaptation strategy that uses inundation over low‐lying areas to reduce tidal range at up‐estuary locations.

Tidal energy budget in the Zhujiang (Pearl River) Estuary

Tidal energy budget in the Zhujiang (Pearl River) Estuary (ZE) is evaluated by employing high-resolution baroclinic regional ocean modeling system (ROMS). The results obtained via applying the least square method on the model elevations are compared against the tidal harmonic constants at 18 tide stations along the ZE and its adjacent coast. The mean absolute errors between the simulation and the observation of M2, S2, K1 and O1 are 4.6, 2.8, 3.2 and 2.8 cm in amplitudes and 9.8°, 15.0°, 4.6° and 4.6° in phase-lags, respectively. The comparisons between the simulated and observed sea level heights at 11 tide gauge stations also suggest good model performance. The total tidal energy flux incoming the ZE is estimated to be 343.49 MW in the dry season and larger than 336.18 MW in the wet season, which should due to higher mean sea level height and heavier density in the dry season. M2, K1, S2, O1 and N2, the top five barotropic tidal energy flux contributors for the ZE, import 242.23 (236.79), 52.97 (52.08), 24.49 (23.96), 16.22 (15.91) and 7.10 (6.97) MW energy flux into the ZE in dry (wet) season, successively and respectively. The enhanced turbulent mixing induced by eddies around isolated islands and sharp headlands dominated by bottom friction, interaction between tidal currents and sill topography or constricted narrow waterways together account for the five energy dissipation hotspots, which add up to about 38% of the total energy dissipation inside the ZE.

Spatial variability in the drag coefficient and its role in tidal dynamics and energetics, a case study: The surface M 2 tide in the subsystem of the Barents and Kara Seas

The QUODDY-4 three-dimensional finite-element hydrostatic model is modified by including a module for the drag coefficient calculated from external determining parameters of the bottom boundary layer (BBL). The modified model is used to evaluate changes in dynamic characteristics (the amplitude and phases of tidal elevations and the maximum barotropic tidal velocity), as well as some components of the barotropic tidal energy budget in the Barents and Kara Seas, induced by the spatial variability in the drag coefficient. It has been shown that the changes in all tidal characteristics, except for the direction of the averaged (over a tidal cycle) horizontal wave transport of barotropic tidal energy, are significant in the sense that they are either greater than the rms absolute vector error or have identical (or near-identical) orders of magnitude when compared to the tidal characteristics themselves. This implies that the concept of a “constant drag coefficient” should be revised.

Tidal characteristics of the gulf of Tonkin

The Gulf of Tonkin, situated in the South China Sea, is a zone of strong ecological, touristic and economic interest. Improving our knowledge of its hydro-sedimentary processes is of great importance to the sustainable development of the area. The scientific objective of this study is to revisit the dominant physical processes that characterize tidal dynamics in the Gulf of Tonkin using a high-resolution model and combination of all available data. Particular attention is thus given to model-data cross-examination using tidal gauges and coastal satellite altimetry and to model calibration derived from a set of sensitivity experiments to model parameters. The tidal energy budget of the gulf (energy flux and dissipation) is then analyzed and its resonance properties are evaluated and compared with idealized models and observations. Then, the tidal residual flow in both Eulerian and Lagrangian frameworks is evaluated. Finally, the problem of tidal frontogenesis is addressed to explain the observed summer frontal structures in chlorophyll concentrations.

Forced tidal response in the Gulf of Mexico

This study investigates the characteristics of tides in the Gulf of Mexico (GoM) and the response to forcing by local tidal potential and tides propagating as waves through straits connecting this semienclosed sea to the Caribbean Sea and Atlantic Ocean. Numerical simulations performed with the Navy Coastal Ocean Model run in a barotropic configuration with 1/60° horizontal resolution are used to analyze the tidal response to different forcing mechanisms. The tidal energy budget and tidal energy fluxes in the GoM are calculated from the simulations. Results show that diurnal tides in the GoM are dominantly due to co‐oscillation with the western Atlantic and that a substantial amount of semidiurnal tidal energy also enters the Gulf through the straits. Model experiments suggest that adding the local tidal potential significantly modifies the propagation of the semidiurnal tidal signal within the GoM and reduces the tidal power associated with the diurnal tides in the basin. An interesting phenomenon of nonlinear interaction between the two forcing mechanisms (local forcing and propagation through the straits) is described and explained by using a mechanistic mass‐spring system model.

Effect of the nonlinear interaction of tidal harmonics on their spatial structure as applied to the system of the white and Barents Seas

Using the three-dimensional nonlinear finite-element thermohydrodynamic model QUODDY-4, we obtain two solutions giving an idea of the role of the nonlinear interaction of tidal harmonics in the formation of their spatial structure. The first solution is induced by the total tide (M2 + S2 + K1 + O1) at the open boundary and by the total static tide inside the area under consideration; then, the solution obtained is subject to harmonic analysis. The second solution is obtained by specifying such tidal sea level elevations at the open boundary that meet individual tidal harmonics. These two solutions are compared. It is shown that the differences between the solutions for the S2, K1, and O1 waves can be significant, especially near the open boundary between the White and Barents seas. This conclusion remains valid also for the maximum velocities (major semiaxes of the ellipses) of the barotropic (depth-average) tidal current as well as for the average (over the tidal cycle) densities of the total tidal energy and components of the tidal-energy budget. The emergence of this feature indicates that there are resonance modes with frequencies that differ from those of the S2, K1, and O1 harmonics to a lesser extent than the M2 harmonic frequency. The same conclusion can be made by comparing the values of the amplification factor, which is defined as the ratio between the actual and static tides, for the system of the Barents and White seas as a whole and for Mezen Bay in the White Sea and Czech Bay in the Barents Sea, taken separately.

Simulation of tides, residual flow and energy budget in the Gulf of California

With the application of a two-dimensional nonlinear hydrodynamical-numerical semi-implicit model, the principal tides M 2, S 2, K 2, N 2, K 1, P 1 and O 1 were studied. Energy budgets of the semi-diurnal M 2 and S 2 were calculated separately. The linear sum of these budgets was compared with the tidal energy budget obtained when these two tidal constituents interact. Since a quadratic form for the bottom friction was used, remarkable differences were found. The results show that in the area of the Colorado River delta, the dissipation of tidal energy is very strong. Intense tidal currents were observed in the same region and over the Salsipuedes Sill. Energy budgets calculated for forcing waves of different periods, but of the same amplitude, were used to estimate the principal periods of resonance. Although the topography of the Gulf is very complex, the model reproduced observed sea-surface elevation and current patterns. To study spring tide conditions, the above seven tidal constituents were simulated. Estimates of residual currents reveal the presence of several intense cyclonic and anticyclonic gyres. Over the Salsipuedes Sill, residual currents of the M 2 tide reach values of more than 15 cm s −1. Horizontal distributions of dissipation rates of tidal energy and of kinetic energy were also obtained.

The flux of tidal energy across latitude 60°S

How and where the ocean tides dissipate their energy are longstanding questions with both oceanographic and astronomical implications. Two decades ago, Doake suggested that flexing of Antarctic ice shelves by the underlying ocean tide is an important energy sink, perhaps accounting for over half the global dissipation rate. Observational constraints on Antarctic dissipation have been scarce. Here two new and complementary ocean‐tide models, both derived from Topex/Poseidon satellite altimeter measurements, are used to determine the flux of tidal energy across 60°S toward the Antarctic coastline. Our results show relatively small fluxes and they therefore rule out Doake's suggestion: Antarctica is an insignificant sink in the global tidal energy budget.

Tidal data inversion: interpolation and inference

Initial efforts in applying inverse methods to studies of ocean tides have focused on making the best use of a small number of observations to map tidal fields in a large area. As such, inversion can be viewed as an objective analysis scheme which uses a dynamically appropriate spatial covariance, derived from the shallow water equations, to interpolate and smooth a sparse data set. Data from recent altimetry missions are not sparsely distributed relative to tidal wavelengths in the open ocean, apparently reducing the need for complicated dynamically based interpolation schemes. Altimetric data sets are also quite large, making application of rigorous inversion methods to global tidal modeling a challenging computational problem. We describe here a new iterative solution scheme which allows us for the first time to fit the full set of TOPEX/Poseidon cross-over differences. The resulting solution (TPXO.3) fits validation tide gauges significantly better than previous inverse solutions. TPXO.3 also reduces residual cross-over variances relative to other recent inverse and empirical solutions, particularly in shallow water where improvements are dramatic. With the new solution approach very significant improvements in global tidal models should be possible in shallow areas and in the vicinity of complex bathymetry, where high-accuracy tidal modeling remains a challenging problem. With the recent improvements in the definition of tidal elevations in the open ocean it should now also be possible to resolve some long unanswered questions about tidal energetics and dynamics. Inverse methods provide a natural framework for addressing these issues, and making inferences about tidal dynamics. In particular, by bringing data and dynamics together in a single solution, we can rigorously test the consistency of the two. We present results of global and local inversions which suggest that over elongated bathymetric features oriented perpendicular to tidal flows, energy dissipation in the open ocean is significantly enhanced, presumably due to conversion of barotropic tidal motions into baroclinic modes. For the M 2 tide our preliminary results suggest that perhaps as much as 0.5 TW of energy is dissipated in this manner. However, due to the simplified linear dynamics and limited spatial resolution used for our inversion, there are significant uncertainties associated with these results. A more careful application of inverse methods to make more rigorous inferences about tidal energetics, including use of more reasonable prior dynamics, and the highest possible spatial resolution, should allow for closure of the tidal energy budget within the next few years.

Model simulations of the M2 and the Kl tide in the Nordic Seas and the Arctic Ocean

The depth-integrated tidal equations have been solved numerically for a model basin covering the North Sea and the Norwegian-Greenland-Barents Seas and the Arctic Ocean. The model is implemented on a stereographic map projection with a grid size 50 times 50 km at 60° N. The semi-diurnal M 2 component and the diurnal K 1 component have been simulated. Correlation coefficients between computed and measured M 2 and K 1 , amplitudes for 116 tidal stations located all around the Nordic Seas were found to be 0.97 and 0.82, respectively. The standard deviation for the corresponding linear regression analysis is ±0.12 m and ±0.02 m, respectively. For the continental shelf along the western coast of Norway and the Barents Sea, the performance of the model is particularly good and the values for the correlation coefficients and standard deviations for this region are 0.97, 0.92, ±0.09 m and ±0.03 m. The M 2 tide is mainly a co-oscillating tide driven by energy influx from the North Atlantic. The K 1 tide is strongly affected by the direct effect of the tide-generating force particularly in the North Sea region and along the coast of western Norway. Different forms of boundary condition along the open boundary towards the North Atlantic have been implemented and tested by comparing the results of the simulation with measurements. Co-range and co-tidal charts are presented and the regional variation of the tidal currents is displayed by maps showing the principal axis of current ellipse and the sense of rotation of the current vector. Energy fluxes are computed for key sections within the model basin and a tidal energy budget for the main parts of the basins is given. DOI: 10.1111/j.1600-0870.1989.tb00367.x

The energy of near‐surface internal waves in the strait of Georgia

Abstract An estimate of the energy content of near‐surface internal waves in the Strait of Georgia is obtained from a combination of aerial photographs and in‐situ measurements. The role of these waves in the tidal energy budget and in the mixing processes in the Strait is discussed.

The Tidal energetics of Narragansett Bay

The average tidal energy budget of Narragansett Bay, a weakly stratified estuary, has been determined from observations of tidal height and current. For average conditions the tidal energy influx to the bay is balanced by the bay's energy sinks, and within the error limits the energy budget balances completely. The average energy inputs to the three bay channels, the West Passage, the East Passage, and the Sakonnet River, are 4.3, 6.4, and 1.1×1013 ergs/s, respectively. Tidal energy is dissipated on the bottom of the bay at the average rate of 8.8×1013 ergs/s, mostly in a few localized areas of high dissipation. The bay does work on the moon at an average rate of 1.8×1013 ergs/s. The energy required for vertical mixing is 0.3×1013 ergs/s. Phase adjustment between tidal height and current is suggested as a mechanism contributing to the instantaneous balance of the tidal energy budget over the lunar cycle.