内潮耗散与自吸-负荷潮对南海潮波影响的数值研究

利用非结构三角形网格的FVCOM海洋数值模式,在其传统二维潮波方程中加入参数化的内潮耗散项和自吸-负荷潮项,计算了南海及其周边海域的M_2、S_2、K_1和O_1分潮的分布。与实测值的比较表明,引入这两项对模拟准确度的提高有明显效果。根据模式结果本文计算分析了研究海域的潮能输入和耗散。能量输入计算表明,能通量是潮能输入的最主要构成部分,通过吕宋海峡断面进入南海的M_2和K_1分潮能通量分别为38和29GW;半日周期的自吸-负荷潮能量输入以负值居多,而全日周期的自吸-负荷潮能量输入以正值居多,因而自吸-负荷潮减弱了南海的半日潮,并加强了南海的全日潮。引潮力的作用也减弱了半日潮而加强了全日潮,但其作用要小于自吸-负荷潮。潮能耗散的分析显示底摩擦耗散在沿岸浅水区域起主导作用,内潮耗散则主要发生在深水区域。内潮耗散的最大值出现在吕宋海峡,且位于南海之外的海峡东部的耗散量大于位于南海之内的海峡西部的耗散量。对M_2和K_1分潮吕宋海峡的内潮耗散总值分别达到16和23GW。     

Data Assimilation Modeling of the Barotropic Tides in the Korea/Tsushima Strait

During 1999–2000, 13 bottom mounted acoustic Doppler current profilers (ADCPs) and 12 wave/tide gauges were deployed along two lines across the Korea/Tsushima Strait, providing long-term measurements of currents and bottom pressure. Tidally analyzed velocity and pressure data from the moorings are used in conjunction with other moored ADCPs, coastal tide gauge measurements, and altimeter measurements in a linear barotropic data assimilation model. The model fits the vertically averaged data to the linear shallow water equations in a least-squares sense by only adjusting the incoming gravity waves along the boundaries. Model predictions are made for the O₁, P₁, K₁, μ₂, N₂, M₂, S₂, and K₂ tides. An extensive analysis of the accuracy of the M₂ surface-height predictions suggests that for broad regions near the mooring lines and in the Jeju Strait the amplitude prediction errors are less than 0.5 cm. Elsewhere, the analysis suggests that errors range from 1 to 4 cm with the exception of small regions where the tides are not well determined by the dataset. The errors in the model predictions are primarily caused by bias error in the model’s physics, numerics, and/or parameterization as opposed to random errors in the observational data. In the model predictions, the highest ranges in sea level height occur for tidal constituents M₂, S₂, K₁, O₁, and N₂, with the highest magnitudes of tidal velocities occurring for M₂, K₁, S₂, and O₁. The tides exhibit a complex structure in which diurnal constituents have higher currents relative to their sea level height ranges than semi-diurnal constituents.     

Tidal oscillations in the Caspian Sea

Long-term hourly data from 12 tide gauge stations were used to examine the character of tidal oscillations in the Caspian Sea. Diurnal and semidiurnal tidal peaks are well-defined in sea level spectra in the Middle and South Caspian basins. High-resolution spectral analysis revealed that the diurnal sea level oscillations in the Middle Caspian Basin have a gravitational origin, while those in the South Caspian Basin are mainly caused by radiational effects: the amplitude of diurnal radiational harmonic S₁ is much higher than those of gravitational harmonics О₁, P₁, and K₁. In the North Caspian Basin, there are no gravitational tides and only weak radiational tides are observed. A semidiurnal type of tide is predominant in the Middle and South Caspian basins. Harmonic analysis of the tides for individual annual series with subsequent vector averaging over the entire observational period was applied to estimate the mean amplitudes and phases of major tidal constituents. The amplitude of the M₂ harmonic reaches 5.4 cm in the South Caspian Basin (at Aladga). A maximum tidal range of 21 cm was found at the Aladga station in the southeastern part of the Caspian Sea, whereas the tidal range in the western part of the South Caspian Basin varies from 5 to 10 cm.     

Phase distribution of tidal constituents around New Zealand

The phase distributions of the M₂, S₂, K₁, and O₁ tidal constituents around New Zealand are plotted from existing harmonic analyses of tidal heights. Both semidiurnal constituents exhibit a complete 360° range of phase around New Zealand, with complex areas of rapid phase change through or near the strait separating the two main islands. The K₁ amphidrome and that for O₁, which previously were thought to be centred on New Zealand, are shown to be located cast of New Zealand. The distributions plotted highlight areas where tidal observations are lacking.     

Observed and modelled tidal currents in the New Zealand region

Tidal currents derived from current meter measurements are compared with the output from a barotropic tidal model of the New Zealand region. For the semi‐diurnal constituents there was very good agreement for the M₂ tide and good agreement for the S₂ tide. For the diurnal constituents (K_l, O_l) it was found that as the amplitude of the constituents decreased so did both the model/observation agreement and the accuracy of the observed tidal ellipse parameters. Consequently it was not possible to decide whether differences arose through shortcomings in the model or in the data. However, the overall performance of the model as a prognostic tool for ocean tidal current simulation appears to be good.     

南麂岛附近海域潮汐和潮流的特征

以2008年冬季在浙江近海南麂岛附近投放的4个底锚系观测的水位和流速资料为依据,分析了潮汐和潮流特征。水位谱分析结果显示半日分潮最显著,全日分潮其次;近岸的浅水分潮比离岸大。水位调和分析结果表明:潮汐类型均为正规半日潮,近岸处的平均潮差大于3m,最大可能潮差大于6m,潮汐呈现出显著的低潮日不等和回归潮特征。流速谱分析结果显示半日分潮流最强,全日分潮流其次,且比半日分潮流小得多;近岸浅水分潮流比远离岸显著。流速调和分析结果表明:潮流类型均为正规半日潮流,靠近岸的两个站浅水分潮流较显著;最显著的半日分潮流是M2分潮流,其最大流速介于0.32～0.48m/s之间,全日分潮流均很弱,最大流速小于0.06m/s。M2分潮流均为逆时针旋转,椭圆率越靠近海底越大;最大分潮流流速分布为中上层最大、表层略小、底层最小;最大分潮流流速方向的垂向变化很小,底层比表层略为偏左;最大分潮流流速到达时间随深度的加深而提前,底层比中上层约提前30min。潮流椭圆的垂向分布显示这里的半日分潮流以正压潮流为主;日分潮流则表现出很强的斜压性。     

Circulation pattern and current variations with respect to tidal frequency in the sea near the head of Suruga Bay

Current measurements were conducted 10 m below the sea surface near the head of Suruga Bay intermittently from 1970 to 1978. The circulation pattern is usually counterclockwise; northward along the east coast (off Heda and at the mouth of Uchiura Inlet), westward along the north coast (off Fuji), and southwestward along the west coast (off Shimizu). The amplitudes of the four major tidal constituents of current variation, M₂, S₂, K₁ and O₁, are much larger than those expected from sea level variations along the coast. The amplitudes of the diurnal constituents of current variation are much larger than those of the semidiurnal constituents, while the amplitudes of the semidiurnal constituents of sea level variation are much larger than those of the diurnal constituents. The observed amplitude of the predominant diurnal constituents exhibit large seasonal changes and tend to increase with the development of the stratification of the upper part of the water in Suruga Bay. These facts strongly suggest that the observed current variations are mainly associated with internal tides in Suruga Bay.     

Cotidal charts and tidal power input atlases of the global ocean from TOPEX/Poseidon and JASON-1 altimetry

The global distributions of eight principal tidal constituents, M₂ , S₂ , K₁ , O₁ , N₂ , K₂ , P₁ , and Q₁ , are derived using TOPEX/Poseidon and JASON-1（T/P-J） satellite altimeter data for 16 a. The intercomparison of the derived harmonics at 7000 subsatellite track crossover points shows that the root mean square （RMS） values of the tidal height differences of the above eight constituents range from 1.19 cm to 2.67 cm, with an average of about 2 cm. The RMS values of the tidal height differences between T/P-J solutions and the harmonics from ground measurements at 152 tidal gauge stations for the above constituents range from 0.34 cm to 1.08 cm, and the relative deviations range from 0.031 to 0.211. The root sum square of the RMS differences of these eight constituents is 2.12 cm, showing the improvement of the present model over the existing global ocean tidal models. Based on the obtained tidal model the global ocean tidal energetics is studied and the global distribution of the tidal power input density by tide-generating force of each constituent is calculated, showing that the power input source regions of semidiurnal tides are mainly concentrated in the tropical belt between 30 S and 30 N, while the power input source regions of diurnal tides are mainly concentrated off the tropic oceans. The global energy dissipation rates of the M₂ , S₂ , K₁ , O₁ , N₂ , P₁ , K₂ and Q₁ tides are 2.424, 0.401, 0.334, 0.160, 0.113, 0.035, 0.030 and 0.006 TW, respectively. The total global tidal dissipation rate of these eight constituents amounts to 3.5 TW.     

A study of non-linear tidal propagation in shallow inlet/estuarine systems Part I: Observations

The offshore tide becomes strongly distorted as it propagates into shallow estuarine systems. Observations of sea surface elevation and horizontal currents over periods ranging from three days to one year, at nine stations within Nauset inlet/estuary, document the non-linear interaction of the off-shore equilibrium tidal constituents. Despite strong frictional attenuation within the estuary, the overtides and compound tides of M₂, S₂ and N₂, in particular, reach significant amplitude, resulting in strong tidal distortion. High frequency forced constituents in sea surface are phase-locked, consistently leading the forcing tides by 60–70°, resulting in a persistent distortion where falling tide is longer than rising tide. Forced constituents in currents are more nearly in phase with equilibrium constituents, producing flood currents which are shorter but more intense than ebb currents. A compound fortnightly tide, MS_f, modulates the mean water level such that lowest tides occur during neap phase instead of spring phase. This fortnightly tide can be contaminated by storm surge, changing the phase characteristics of this constituent. Implications of the overtides, compound tides, and lower frequency tides on near-bed, suspended and dissolved material transport are profound.     

Mode-1 internal tides in the western North Atlantic Ocean

Mode-1 internal tides were observed the western North Atlantic using an ocean acoustic tomography array deployed in 1991–1992 centered on 25°N, 66°W. The pentagonal array, 700-km across, acted as an antenna for mode-1 internal-tides. Coherent internal-tide waves with O(1 m) displacements were observed traveling in several directions. Although the internal tides of the region were relatively quiescent, they were essentially phase locked over the 200–300 day data record lengths. Both semidiurnal and diurnal internal waves were detected, with wavenumbers consistent with those calculated from hydrographic data. The M₂ internal-tide energy flux was estimated to be about 70 W m⁻¹, suggesting that mode-1 waves radiate 0.2 GW of energy, with large uncertainty, from the Caribbean island chain at this frequency. A global tidal model (TPXO 5) suggested that 1–2 GW is lost from the M₂ barotropic tide over this region, but the precise value was uncertain because the complicated topography makes the calculation problematic. In any case, significant conversion of barotropic to baroclinic tidal energy does not occur in the western North Atlantic basin. It is apparent, however, that mode-1 internal tides have very weak decay and retain their coherence over great distances, so that ocean basins may be filled up with such waves. Observed diurnal amplitudes were an order of magnitude larger than expected. The amplitude and phase variations of the K₁ and O₁ constituents observed over the tomography array were consistent with the theoretical solutions for standing internal waves near their turning latitude. The energy densities of the resonant diurnal internal waves were roughly twice those of the barotropic tide at those frequencies.     

泰国湾及邻近海域潮汐潮流的数值模拟

本文基于FVCOM(Finite-Volume Coastal Ocean Model)模式,模拟了泰国湾及其周边海域K1、O1、M2和S2四个主要分潮。采用47个验潮站实测调和常数与模拟结果进行比较,所得4个分潮的均方差分别为4.06cm、3.76cm、8.22cm和4.71cm,符合良好。根据计算结果分析了泰国湾及其周边海域的潮汐、潮流的分布特征和潮波的传播特征。数值试验表明,现有的数字水深资料(ETOPO1,ETOPO5,DBDB-V)的准确度不足以合理地模拟泰国湾潮波。     

西北太平洋的一种潮汐数值同化模型

利用FVCOM海洋数值模式,在球坐标系统下考虑非线性效应和天体引潮力的影响,基于非结构的三角形网格建立了包括中国近海、日本海、鄂霍次科海和部分西北太平洋海域的高分辨率海洋潮汐数值模型,并采用趋近法同化84个沿岸验潮站的观测资料。模拟结果与175个验潮站的实测结果拟合良好,M₂,S₂,K₁,O₁四个主要分潮振幅和迟角的绝对平均误差分别为4.0 cm和5.6°,2.4 cm和7.5°,2.6 cm和6.3°,1.5 cm和5.0°。依据调和分析结果给出了4个主要分潮的同潮图分布,得到8个半日分潮和5个全日分潮的无潮点,证实了宗谷海峡全日潮无潮点的存在,首次模拟得到津轻海峡的全日潮无潮点;还给出了整个计算海域内最大可能潮差和潮汐余水位的分布特征。     

胶州湾潮汐潮流动边界数值模拟

基于普林斯顿海洋模式,通过干湿网格判别法引入潮汐潮流的漫滩过程,考虑M₂,S₂,K₁,O₁,M₄和MS₄六个主要分潮,建立了胶州湾潮汐潮流数值模拟和预报模型,研究了该海域潮汐潮流特征,并讨论了漫滩对潮流模拟的影响。与实测资料的对比验证表明,该模式能够对胶州湾的潮汐和潮流做出较为合理的预测。给出了胶州湾潮汐、潮流、余流等分布特征,模拟的潮流场以及余流场涡旋等现象与观测符合良好;计算了潮波能通量,从能量角度探讨了潮波的传播特性;对潮位与潮流场演变规律,以及潮能通量的分析表明,胶州湾内的潮波以驻波为主。通过数值试验发现,漫滩过程的引入对胶州湾潮流速度的模拟至关重要,不考虑漫滩过程的模式会夸大或者低估潮流流速。对于滩涂面积广阔的海域来说,潮流数值模式中考虑漫滩的影响是必要的。     

Anomalous amplifications of semidiurnal tides along the western coast of Taiwan

By compiling all the tidal data gathered from island-wide results of simple harmonic analysis, anomalous amplifications of semidiurnal tides along the western coast of Taiwan are illustrated. The mechanisms are investigated both theoretically and numerically by applying the linear shallow-water wave equations. Waves trapped by a continental shelf and resonance of tidal co-oscillation are identified theoretically. Numerically, a two-dimensional finite element model is applied to real topography for tidal computations. The co-range and equi-phase charts of three main semidiurnal constituents (M₂, S₂, and N₂) and one diurnal constituent K₁ are calculated. Anomalous amplifications of semidiurnal tides that appear as partially standing waves are demonstrated.     

粤西沿岸海域潮汐特征

对粤西海域水东、湛江、硇州岛、南渡和海安验潮站各1年水位资料进行了调和分析及统计。结果表明:粤西海域北部湛江、水东、硇洲岛、南渡4站主要分潮为M_2、K_1、S_2和O_1,是不规则半日潮;而南部海安站主要分潮为O_1和K_1分潮,是不规则日潮。粤西沿岸各站浅水分潮和平均水位从北到南有减小趋势。在日潮不等方面,粤西沿岸验潮站都存在明显的日潮高、日潮时不等现象。日潮时不等总体上从北到南有降低的趋势,北部湛江、水东和硇州岛涨潮时间比落潮长1~1.5 h,南部南渡和海安两站涨、落潮时相差不大。另外,调和分析和经验公式不再适用于南渡站,南渡河入海口处堤闸工程是主要原因。这为粤西海域环境资源开发、航运活动等提供环境支持和保障。     

Characteristics of Tides in the Bay of Bengal

A vertically integrated 2D numerical model was developed for the simulation of major tidal constituents (M₂, S₂, N₂, K₁ and O₁) in the Bay of Bengal. The bathymetry for the model domain was derived from an improved ETOPO5 dataset prepared in our earlier work. The simulated tidal elevations showed good agreement with the hourly tide gauge observations at Paradip, Visakhapatnam, and Chennai. The amplitudes and phases of M₂, S₂, K₁, and O₁ at the coastal stations, obtained from harmonic analysis of simulated tides, were found to agree well with those obtained from Admiralty Tide Tables with the RMS misfit 9.2, 5.6, 2.9 and 3.1 cm, respectively. In the Bay of Bengal, semi-diurnal tides (M₂, S₂, and N₂) attain highest amplitudes (180, 80, 30 cm, respectively) in the Gulf of Martaban while amplitudes of diurnal tides (K₁, O₁) reaches maximum (20, 12 cm, respectively) in the Malacca Strait. The continental shelf in the head bay and along the southern coast of Myanmar is about 200 km wide and the amplitudes of semi-diurnal tides are doubled in these regions while the diurnal tides amplify only marginally, which is consistent with Clarke and Battisti theory. In the north eastern end of the head bay and the Gulf of Martaban, the geometrical configuration of the coastline, in addition to the wide continental shelf, could contribute to the amplification of both semi-diurnal and diurnal constituents. In the Malacca Strait, the amplitudes of both semi-diurnal and diurnal tides are found to increase gradually from the northern end to the 2.5°N and decreases towards southern boundary. The co-tidal and co-range charts of M₂ and S₂ tidal constituents also show the presence of two degenerate amphidromic points in the head bay. A virtual amphidromic point for M₂ is identified in the Malacca Strait.     

北部湾潮波数值研究

利用普林斯顿海洋模式(POM08)建立了北部湾及其临近海区潮汐潮流数值模式,模拟了K1,O1,M2和S2这4个主要分潮,分析了模拟的潮汐和潮流分布特征,从潮波能量的角度讨论了琼州海峡对北部湾潮波系统的影响,并给出北部湾潮能的耗散情况。研究表明,北部湾是典型的全日潮海区,K1和O1分潮在南部湾口形成半个旋转潮波系统,无潮点位于越南顺安附近岸边。琼州海峡中的欧拉潮汐余流为西向流,潮余流造成的水通量约为0.034×106m3/s;余流出海峡西口后,先折向北,然后转向南流出湾外。研究海区中两个强潮流区分别位于琼州海峡和海南岛的西侧,同时这也是两个潮能的高耗散区。北部湾的潮能自南部湾口由外海传入,通过西口涌入琼州海峡,到达海峡东口时日潮波的能量已基本耗散殆尽,在海峡内耗散的4个分潮的潮能约为3.33 GW,相当于北部湾潮能耗散量的35%左右。数值试验表明,琼州海峡作为潮能耗散的重要海区,其存在对于北部湾潮波系统的形成具有较大影响。计算了底边界潮能耗散,结果表明在北部湾和琼州海峡,底边界耗散的潮能分别占该海区总耗散的83%和80%。     

Numerical study of tidal dynamics in the South China Sea with adjoint method

We adopt a parameterized internal tide dissipation term to the two-dimensional (2-D) shallow water equations, and develop the corresponding adjoint model to investigate tidal dynamics in the South China Sea (SCS). The harmonic constants derived from 63 tidal gauge stations and 24 TOPEX/Poseidon (T/P) satellite altimeter crossover points are assimilated into the adjoint model to minimize the deviations of the simulated results and observations by optimizing the bottom friction coefficient and the internal tide dissipation coefficient. Tidal constituents M₂, S₂, K₁ and O₁ are simulated simultaneously. The numerical results (assimilating only tidal gauge data) agree well with T/P data showing that the model results are reliable. The co-tidal charts of M₂, S₂, K₁ and O₁ are obtained, which reflect the characteristics of tides in the SCS. The tidal energy flux is analyzed based on numerical results. The strongest tidal energy flux appears in the Luzon Strait (LS) for both semi-diurnal and diurnal tidal constituents. The analysis of tidal energy dissipation indicates that the bottom friction dissipation occurs mainly in shallow water area, meanwhile the internal tide dissipation is mainly concentrated in the LS and the deep basin of the SCS. The tidal energetics in the LS is examined showing that the tidal energy input closely balances the tidal energy dissipation.     

Oceanic tidal angular momentum and Earth's rotation variations

Luni-solar tides affect Earth's rotation in a variety of ways. We give an overview of the physics and focus on the excitation of Earth rotational variations by ocean tides under the conservation of angular momentum. Various models for diurnal and semidiurnal tidal height and tidal current fields have been derived, following a legacy of a number of theoretical tide models, from the Topex/Poseidon (T/P) ocean altimetry data. We review the oceanic tidal angular momenta (OTAM) predicted by these T/P models for the eight major tides (Q₁, O₁, P₁, K₁, N₂, M₂, S₂, K₂), and their excitations on both Earth's rotational speed variation (in terms of length-of-day or UT1) and polar motion (prograde diurnal/semidiurnal components and retrograde semidiurnal components). These small, high-frequency effects have been unambiguously observed in recent years by precise Earth rotation measurements via space geodetic techniques. Here we review the comparison of the very-long-baseline-interferometry (VLBI) data with the T/P OTAM predictions. The agreement is good with discrepancies typically within 1 – 2 microseconds for UT1 and 10 – 30 microarcseconds for polar motion. The eight tides collectively explain the majority of subdaily Earth rotation variance during the intensive VLBI campaign Cont94. This establishes the dominant role of OTAM in exciting the diurnal/semidiurnal polar motion and paves the way for detailed studies of short-period non-OTAM excitations, such as atmospheric and oceanic angular momentum variations, earthquakes, the atmospheric thermal tides, Earth librations, and the response of the mantle lateral inhomogeneities to tidal forcing. These studies await further improvements in tide models and Earth rotation measurements.     

Numerical study of baroclinic tides in Luzon Strait

The spatial and temporal variations of baroclinic tides in the Luzon Strait (LS) are investigated using a three-dimensional tide model driven by four principal constituents, O₁, K₁, M₂ and S₂, individually or together with seasonal mean summer or winter stratifications as the initial field. Barotropic tides propagate predominantly westward from the Pacific Ocean, impinge on two prominent north-south running submarine ridges in LS, and generate strong baroclinic tides propagating into both the South China Sea (SCS) and the Pacific Ocean. Strong baroclinic tides, ∼19 GW for diurnal tides and ∼11 GW for semidiurnal tides, are excited on both the east ridge (70%) and the west ridge (30%). The barotropic to baroclinic energy conversion rate reaches 30% for diurnal tides and ∼20% for semidiurnal tides. Diurnal (O₁ and K₁) and semidiurnal (M₂) baroclinic tides have a comparable depth-integrated energy flux 10–20 kW m⁻¹ emanating from the LS into the SCS and the Pacific basin. The spring-neap averaged, meridionally integrated baroclinic tidal energy flux is ∼7 GW into the SCS and ∼6 GW into the Pacific Ocean, representing one of the strongest baroclinic tidal energy flux regimes in the World Ocean. About 18 GW of baroclinic tidal energy, ∼50% of that generated in the LS, is lost locally, which is more than five times that estimated in the vicinity of the Hawaiian ridge. The strong westward-propagating semidiurnal baroclinic tidal energy flux is likely the energy source for the large-amplitude nonlinear internal waves found in the SCS. The baroclinic tidal energy generation, energy fluxes, and energy dissipation rates in the spring tide are about five times those in the neap tide; while there is no significant seasonal variation of energetics, but the propagation speed of baroclinic tide is about 10% faster in summer than in winter. Within the LS, the average turbulence kinetic energy dissipation rate is O(10⁻⁷) W kg^{− 1} and the turbulence diffusivity is O(10⁻³) m²s⁻¹, a factor of 100 greater than those in the typical open ocean. This strong turbulence mixing induced by the baroclinic tidal energy dissipation exists in the main path of the Kuroshio and is important in mixing the Pacific Ocean, Kuroshio, and the SCS waters.