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1.
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. 相似文献
2.
《Continental Shelf Research》1987,7(10):1181-1209
The quadratic law of bottom friction demands an increased frictional coefficient for the S2 and N2 tides with respect to a dominant M2 tidal signal. A numerical model of the semidiurnal tides in the northeast Atlantic gives an increase in friction of ∼35% for the N2, S2 and K2 tides with respect to the M2 tide and this value is close to a theoretically derived estimate for the region, providing confirmation of the general widescale applicability of the quadratic friction law. Small differences in friction also occur for the N2, S2 and K2 tides and this is attributed to the interaction of the L2 and μ2 tides with the M2 tide in the presence of quadratic friction. Energy dissipation relationships, anomalous K2/S2 amplitude ratios and the role of quadratic friction on 18.6 year variations of semidiurnal forcing are examined. 相似文献
3.
A two-dimensional vertically integrated model of the North Sea is used to compute the distribution of M2 and M4 tidal elevations and currents over the region. Comparison of computed and observed elevations and currents in the area shows that the model can accurately reproduce the M2 tide in the North Sea, although there are difficulties with the M4 tide particularly in the northern North Sea.Comparison between model and a large number of observations collected in a shallow water region off the east coast of England, revealed that the model can accurately reproduce the tides even in near coastal regions, where model resolution problems can occur. Comparisons of computed and observed M2 tidal energy fluxes in this region, show that model and observations agree to within the order of 10% (the error associated with the necessary interpolation of the observations in order to compute the energy flux).The problem of computing energy dissipation in the area by subtracting the energy fluxes into and out of the region is shown to be ill-conditioned in that the energy dissipation in the area is comparable to the error in the energy flux. Consequently for the sea region considered here it is not meaningful to compare this energy budget with energy dissipation due to bottom friction.Energy dissipation for the whole of the North Sea is computed using the numerical model and the geographical distribution of dissipation due to bottom friction is given for the M2 tide. 相似文献
4.
The mean sea level and mean bed stress due to tidal co-oscillations in the presence of quadratic friction is examined analytically and numerically. In some idealised situations under conditions of near M4 shelf resonances it is shown that phase relationships tend to exist between the M2 tidal currents and the M4 tidal currents which combine to give maximum currents in the flood or ebb direction. In the presence of quadratic friction these effects result in a mean bed stress and affect mean sea level. It is shown that these idealised responses are in part relevant to the sea level differences and sand transport paths due to tides around the British Isles. 相似文献
5.
《Continental Shelf Research》1998,18(7):739-772
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. 相似文献
6.
Non-linear tidal constituents, such as the overtide M4 or the compound tide MS4, are generated by interaction in shallow seas of the much larger astronomically forced “primary” tidal constituents (e.g., M2, S2). As such, errors in modeling these “secondary” shallow-water tides might be expected to be caused first of all by errors in modeling the primary constituents. Thus, in the context of data assimilation, observations of primary-constituent harmonic constants can indirectly constrain shallow-water constituents. Here we consider variational data assimilation for primary and secondary tidal constituents as a coupled problem, using a simple linearized perturbation theory for weak interactions of the dominant primary constituents. Variation of the resulting penalty functional leads to weakly non-linear Euler–Lagrange equations, which we show can be solved approximately with a simple two-stage scheme. In the first stage, data for the primary constituents are assimilated into the linear shallow water equations (SWE), and the resulting inverse solutions are used to compute the quadratic interactions in the non-linear SWE that constitute the forcing for the secondary constituents. In the second stage, data for the compound or overtide constituent are assimilated into the linear SWE, using a prior forced by the results of the first stage. We apply this scheme to assimilation of TOPEX/Poseidon and Jason altimetry data on the Northwest European Shelf, comparing results to a large set of shelf and coastal tide gauges. Prior solutions for M4, MS4 and MN4 computed using inverse solutions for M2, S2, and N2 dramatically improve fits to validation tide gauges relative to unconstrained forward solutions. Further assimilation of along-track harmonic constants for these shallow-water constituents reduces RMS differences to below 1 cm on the shelf, approaching the accuracy of the validation tide gauge harmonic constants. 相似文献
7.
This study examines connections between mean sea level (MSL) variability and diurnal and semidiurnal tidal constituent variations at 17 open-ocean and 9 continental shelf tide gauges in the western tropical Pacific Ocean, a region showing anomalous rise in MSL over the last 20 years and strong interannual variability. Detrended MSL fluctuations are correlated with detrended tidal amplitude and phase fluctuations, defined as tidal anomaly trends (TATs), to quantify the response of tidal properties to MSL variation. About 20 significant amplitude and phase TATs are found for each of the two strongest tidal constituents, K1 (diurnal) and M2 (semidiurnal). Lesser constituents (O1 and S2) show trends at nearly half of all gauges. Fluctuations in MSL shift amplitudes and phases; both positive and negative responses occur. Changing overtides suggest that TATs are influenced by changing shallow water friction over the equatorial Western Pacific and the eastern coast of Australia (especially near the Great Barrier Reef). There is a strong connection between semidiurnal TATs at stations around the Solomon Islands and changes in thermocline depth, overtide generation, and the El Niño Southern Oscillation (ENSO). TATs for O1, K1, and M2 are related to each other in a manner that suggests transfer of energy from M2 to the two diurnals via resonant triad interactions; these cause major tidal variability on sub-decadal time scales, especially for M2. The response of tides to MSL variability is not only spatially complex, it is frequency dependent; therefore, short-term responses may not predict long-term behavior. 相似文献
8.
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. 相似文献
9.
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 O1, 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 相似文献
10.
《Advances in water resources》1987,10(3):138-148
The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O1, K1, M2, S2, N2, K2, M4, MS4, MN4, M6, and 2MS6. 相似文献
11.
Observations at 8 sites in the outer central Great Barrier Reef show M2, S2, K1, and O1 tidal currents flow directly off-shelf (northeast), when the corresponding tide at Townsville is at zero height and falling, with typical amplitudes of 12, 6, 3, and 2 cm s?1. On the slope (at 300 m depth), the vertically averaged long-shelf component was small. On the shelf, the eccentricity of the tidal ellipses decreases shoreward and the tidal ellipses rotate anticlockwise. The major axes of the tidal ellipses tilt left of cross-shelf, especially for the diurnal constituents. There is satisfactory agreement between the observed and modelled cross-shelf currents. The long-shelf velocity is sensitive to the long-shelf changes in amplitude and phase of the tide heights and high quality tidal data for open boundary conditions will be required if numerical models are to model these currents satisfactorily. 相似文献
12.
Oleg Zaytsev Alexander B. Rabinovich Richard E. Thomson Norman Silverberg 《Continental Shelf Research》2010
Currents in the northern Bay of La Paz were examined using an 8-month Acoustic Doppler Current Profiler (ADCP) record collected in the upper 185 m of the water column during 2007. Flow variability was dominated by tidal motions, which accounted for 43% (33% diurnal, 10% semidiurnal) of the total kinetic energy. The tidal motions had a pronounced vertical structure dominated within a shallow (∼30 m thick) surface layer by intense counterclockwise (CCW) rotary S1 diurnal radiational currents that were highly coherent with the counterclockwise seabreeze. Motions within the semidiurnal frequency band were primarily associated with significant counterclockwise S2 radiational tidal currents, which were also coherent with the seabreeze. Both S1 and S2 tidal ellipses in the upper layer were aligned perpendicular to the bay entrance with mean semi-major axes of 55 and 20 cm/s, respectively. Below the surface layer, tidal currents decayed rapidly to relatively weak, clockwise rotary barotropic motions. In contrast to those for radiational harmonics, tidal ellipses of the gravitational constituents (M2, K1 and O1) were oriented cross-bay. Energy within the diurnal frequency band in the surface layer was dominated by a coherent component (barotropic, phase-locked baroclinic and radiational), which accounted for roughly 65% (59% from S1 alone) of the total diurnal kinetic energy. Of the remaining diurnal band energy, 18% was associated with an incoherent baroclinic component and 17% with a background noise component. Below 30 m depth, the corresponding estimates are 40%, 32% and 28%, respectively. The persistent, surface-intensified CCW rotary currents observed at the mooring site are assumed to be forced by strong CCW seabreeze winds in the presence of a “slippery” low-density surface layer. This response may be further augmented by topographic narrowing at the bay entrance and by the close proximity of the diurnal and inertial frequency bands in the region. 相似文献
13.
《Continental Shelf Research》1999,19(14):1771-1782
In the Gulf of Kutch on the northwestern shelf of India the semi-diurnal constituents M2 and S2 get amplified approximately threefold. In contrast, amplification of the diurnal constituents K1 and O1 is small. From analytical and numerical solutions of linear, viscous, cross-sectionally averaged equations for tidal motion in a channel, it is seen that the observed amplification results from a combination of quarter-wavelength resonance, geometric effect due to decrease in width of the channel, and friction. 相似文献
14.
Tidal currents,energy flux and bottom boundary layer thickness in the Clyde Sea and North Channel of the Irish Sea 总被引：2，自引：0，他引：2
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 相似文献
15.
Tjebbe M. Hepkema Huib E. de Swart Antonios Zagaris Matias Duran–Matute 《Ocean Dynamics》2018,68(4-5):439-455
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. 相似文献
16.
Robin Robertson 《Ocean Dynamics》2006,56(5-6):430-444
Terrain-following ocean models are being used to simulate baroclinic tides and provide estimates of the tidal fields for circulation
and mixing studies. These models have successfully reproduced elevations with most of the remaining inaccuracies attributed
to topographic errors; however, the replication of barotropic and baroclinic velocity fields has not been as robust. Part
of the problem is the lack of an adequate observational dataset in the simulated regions to compare the models. This problem
was addressed using a dataset collected during the Flow over Abrupt Topography initiative at Fieberling Guyot. To evaluate
the capability of the Regional Ocean Model System (ROMS) to simulate baroclinic tidal velocities, the combined tides for four
constituents, M2, S2, K1, and O1, were modeled over Fieberling Guyot. Model inputs, numerical schemes, and parameterizations were varied to improve agreement
with observations. These included hydrography, horizontal resolution, and the vertical mixing parameterization. Other factors
were evaluated but are not included in this paper. With the best case, semidiurnal baroclinic tides were well replicated with
RMS differences between the model estimates and the observations of 1.85 and 0.60 cm s−1 for the major axes of the tidal ellipses for M2 and S2, respectively. However, diurnal K1 baroclinic tides were poorly simulated with RMS differences of 4.49 cm s−1. In the simulations, the K1 baroclinic tides remained bottom-trapped unlike the observed fields, which had free waves due to the contribution of the
mean velocity to the potential vorticity. The model did not adequately simulate the mean velocity, and the K1 tides remained trapped. A resolution of 1 km most accurately reproduced the major axes and mean velocities; however, a 4-km
resolution was sufficient for a qualitative estimate of where baroclinic tidal generation occurred. Nine vertical mixing parameterizations
were compared. The vertical mixing parameterization was found to have minor effects on the velocity fields, with most effects
occurring over the crown of guyot and in the lower water column; however, it had dramatic effects on the estimation of vertical
diffusivity of temperature. Although there was no definitive best performer for the vertical mixing parameterization, several
parameterizations could be eliminated based on comparison of the vertical diffusivity estimates with observations. The best
performers were Mellor–Yamada and three generic length scale schemes. 相似文献
17.
Kyoko Ohashi Jinyu Sheng Keith R. Thompson Charles G. Hannah Harold Ritchie 《Ocean Dynamics》2009,59(6):809-825
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. 相似文献
18.
The signal to noise ratio in tidal data in the diurnal and semidiurnal frequency bands is ordinarily so large that the noise contribution to the tidal harmonic constants is unimportant. However, as the observational locations are selected progressively closer to an amphidrome (point of no tide), the signal to noise ratio decreases, making the tidal harmonic constants less dependable. Standard deviations in amplitude of M2 and S2 obtained from 12 29-day analyses of a year of tide data obtained at a standard tide station, estimated to be 280 and 550 km away from the amphidromes for these constituents in the eastern Caribbean, are roughly one-third of the mean amplitudes for these constituents; the standard deviations in epoch are 38° and 30° respectively. Therefore, a program to locate an amphidrome precisely is self-defeating and the location can only be approximated by a grid of tide observations spanning the geographic position and/or by longer series of observations, using higher resolution to increase the signal to noise ratio. Amplitudes of 0.64 cm and 1.24 cm were calculated for M2 and S2 from a one-month series of pelagic observations obtained very close to an inferred position of the M2 amphidrome in the northeast Caribbean Sea.Abbreviations C&GS
Coast and Geodetic Survey
- CICAR
Cooperative Investigation of the Caribbean and Adjacent Regions
- IAPSO
International Association for the Physical Sciences of the Ocean
- ICOT
Institute of Coastal Oceanography and Tides
- IDOE
International Decade of Ocean Exploration
- NOAA
National Oceanic and Atmospheric Administration
- NOS
National Ocean Survey
- NSF
National Science Foundation
- SCOR
Scientific Committee of Oceanic Research
- UNESCO
United Nations Educational, Scientific, and Cultural Organization 相似文献
19.
The tidal dynamics in a pristine, mesotidal (>2 m range), marsh-dominated estuary are examined using moored and moving vessel field observations. Analysis focuses on the structure of the M
2 tide that accounts for approximately 80% of the observed tidal energy, and indicates a transition in character from a near standing wave on the continental shelf to a more progressive wave within the estuary. A slight maximum in water level (WL) occurs in the estuary 10–20 km from the mouth. M
2 WL amplitude decreases at 0.015 m/km landward of this point, implying head of tide approximately 75 km from the mouth. In contrast, tidal currents in the main channel 25 km inland are twice those at the estuary mouth. Analysis suggests the tidal character is consistent with a strongly convergent estuarine geometry controlling the tidal response in the estuary. First harmonic (M
4) current amplitude follows the M
2 WL distribution, peaking at mid-estuary, whereas M
4 WL is greatest farther inland. The major axis current amplitude is strongly influenced by local bathymetry and topography. On most bends a momentum core shifts from the inside to outside of the bend moving seaward, similar to that seen in unidirectional river flow but with point bars shifted seaward of the bends. Dissipation rate estimates, based on changes in energy flux, are 0.18–1.65 W m−2 or 40–175 μW kg–1. A strong (0.1 m/s), depth-averaged residual flow is produced at the bends, which resembles flow around headlands, forming counter-rotating eddies that meet at the apex of the bends. A large sub-basin in the estuary exhibits remarkably different tidal characteristics and may be resonant at a harmonic of the M
2 tide. 相似文献
20.
The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic M2 amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power consumption. 相似文献