On the variability of tidal constants induced by the influence of one subsystem on another

It is stated that the seasonal variation of tidal constants may be generated through a mechanism related to the influence of one subsystem on another. This statement is verified on the basis of the three-dimensional nonlinear finite-element thermohydrodynamic model QUODDY-4, which is used to investigate the tidal dynamics of the wave M ₂ in the system of the White and Barents seas. It is testified that the freezing of the White Sea and the resulting fixed ice cover change the tidal characteristics in the other subsystem—the nonfreezing Barents Sea. Here (especially, in the southern part of the Barents Sea, adjacent to the boundary of the White Sea), the relative variations in the amplitude of tidal sea surface level elevations and the maximum barotropic tidal velocity may constitute up to 75%, and the variation in phases of tidal sea surface level elevations may cover a few tens of degrees. It follows that the seasonal variability of tidal constants induced by the influence of one subsystem on another may in principal occur and there are no good grounds for its disregard, as has been done usually.     

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 (M ₂ + S ₂ + K ₁ + O ₁) 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 S ₂, K ₁, and O ₁ 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 S ₂, K ₁, and O ₁ harmonics to a lesser extent than the M ₂ 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.     

Three-dimensional modeling of tidal circulation and mixing over the Java Sea

A combination of a three-dimensional hydrodynamic model and in-situ measurements provides the structures of barotropic tides, tidal circulation and their relationship with turbulent mixing in the Java Sea, which allow us to understand the impact of the tides on material distribution. The model retains high horizontal and vertical resolutions and is forced by the boundary conditions taken from a global model. The measurements are composed of the sea level at coastal stations and currents at moorings embedded in Seawatch buoys, in addition to hydrographic data. The simulated tidal elevations are in good agreement with the data for the K₁ and M₂ constituents. The K₁ tide clearly shows the lowest mode resonance in the Java Sea with intensification around the nodal point in the central region. The M₂ tide is secondary and propagates westward from the eastern open boundary, along with a counterclockwise amphidromic point in the western part. The K₁ tide produces a major component of tidal energy, which flows westward and dissipates through the node region near the Karimata Strait. Meanwhile, the M₂ tide dissipates in the entire Java Sea. However, the residual currents are mainly induced by the M₂ tide, which flows westward following the M₂ tidal wave propagation. The tidal mixing is mainly caused by K₁ tide which peaks at the central region and is consistent with the uniform temperature and salinity along the vertical dimension. This mixing is expected to play an important role in the vertical exchange of nutrients and control of biological productivity.     

Tidal transport through the Tsugaru Strait — part I: Characteristics of the major tidal flow and its residual current

The potential role of the tide-induced time-mean flow (the tidal residual current) in determining transport through the Tsugaru Strait (located between the East/Japan Sea and the North Pacific) is investigated using a high-resolution numerical barotropic model. The calculated K₁, O₁, M₂, and S₂ tidal fields agree well with available observational records derived from both tide gauge and current meter measurements in the strait and the adjacent seas. The tidal residual current speed reaches 0.3 ms⁻¹ in two narrow “neck” areas where topographic sills are located. This result suggests that tides should be taken into account in estimating the long-term water mass and nutrient transport through narrow regions between the East/Japan Sea and the North Pacific. An interesting aspect of the tidal residual current field is the prediction of several active eddy zones in which sequences of eddy triplets develop in the vicinity of capes. Our vorticity analysis reveals that the interplay of topographic effects arising from both the headland and the sill around capes plays a critical role in the formation of these triple eddy patterns.     

Spatial structure of the <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript> tidal wave in the canadian arctic archipelago

The surface M ₂ tide in the Canadian Arctic Archipelago (CAA) is reproduced on the basis of the QUODDY-4 three-dimensional finite-element hydrodynamic model. Particular emphasis has been placed on comparing model estimates for the amplitudes and phases of tidal elevations and the parameters of ellipses (major semiaxis and eccentricity) of the barotropic tidal current velocity with observational data. We present their spatial distributions and the distributions of averaged (over a tidal cycle) values of the density, horizontal transfer, and dissipation rate of barotropic tidal energy. It is found that the CAA is a much less effective dissipator of barotropic tidal energy than the World Ocean.     

Modeling the tidal ice drift and ice-induced changes in tidal dynamics on the Siberian continental shelf

The tidal ice drift is treated as an element of the three-dimensional tidal dynamics in a sea covered by ice. This dynamics is described by the QUODDY-4 finite-element model, and the tidal ice drift is described by a continuous viscous-elastic approximation. We present the results of modeling not only the tidal ice drift (M ₂ wave) (its velocity, direction, and tidal variations in the concentration and pressure of ice compression) but also ice-induced changes in tidal dynamics and the residual tidal ice drift. The modeling results indicate that the maximum velocity of tidal ice drift, which is determined by a combination of various factors responsible for ice evolution and primarily by the horizontal gradient of the level and local tidal velocity, can be higher or lower than the velocity of the surface tidal current in the ice-free sea. This depends on the sign of deviations of tidal sea level elevations in the sea covered by ice from their values in the ice-free sea. In addition, it has been found that ice cover has a stronger effect on the energetics of tides than on their dynamics: the area-mean relative deviations constitute 1.5% for the density of the total tidal energy, 61.5% for the dissipation, 0.1% for the amplitudes of tidal sea level elevations, and 0.9% for the amplitudes of maximum barotropic tidal velocity. In this sense, the conclusion that the role of sea ice is insignificant in the formation of tides can be justified only partially. The main results of this paper are as follows: (1) the development of a module for tidal ice drift, (2) the inclusion of this module into the three-dimensional finite-element hydrothermodynamic model QUODDY-4 to extend its capabilities, and (3) the reproduction (on the basis of the modified model) of qualitative features of the practically important tidal ice drift and ice-induced changes in the tidal dynamics of marginal seas on the Siberian continental shelf.     

吐噶喇海峡内潮的能量收支和大小潮变化

吐噶喇海峡是西北太平洋重要的内潮产生区域,该区域内产生的内潮对于东海陆架和西北太平洋的混合和物质输运有十分重要的作用。水平分辨率为3km的JCOPE-T(JapanCoastalOcean PredictabilityExperiment—Tides)水动力学模式的结果表明,吐噶喇海峡的内潮主要产生在地形变化剧烈的海山和海岛附近,其引起的等密面起伏振幅可达30m。吐噶喇海峡的内潮在垂直于等深线方向分为两支向外传播:一支向西北方向传播,进入东海陆架后迅速减小;另一支向东南方向传播,进入西北太平洋。吐噶喇海峡潮能丰富,其在约半个月内的平均输入的净正压潮能通量为13.92GW,其中约有3.73GW转化为内潮能量。生成的内潮能量有77.2%在当地耗散,传出的内潮能通量为0.84GW,主要通过西北和东南两个边界传出。该区域潮能通量有显著的大小潮变化,大潮期间输入的正压潮净能通量和产生的内潮能通量均约为小潮期间的2倍,但其主要产生区域基本不变,且内潮能量耗散比率均在产生的内潮通量的76%—79%。另外,内潮能通量的传播方向也没有发生变化,仍主要通过西北和东南两个边界传出。因此,大小潮的变化仅影响吐噶喇海峡处产生的内潮能量的大小,不影响其产生区域、传播方向和耗散比率。     

Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea

A three-dimensional tidal current model is developed and applied to the East China Sea (ECS), the Yellow Sea and the Bohai Sea. The model well reproduces the major four tides, namely M₂, S₂, K₁ and O₁ tides, and their currents. The horizontal distributions of the major four tidal currents are the same as those calculated by the horizontal two-dimensional models. With its high resolutions in the horizontal (12.5 km) and the vertical (20 layers), the model is used to investigate the vertical distributions of tidal current. Four vertical eddy viscosity models are used in the numerical experiments. As the tidal current becomes strong, its vertical shear becomes large and its vertical profile becomes sensitive to the vertical eddy viscosity. As a conclusion, the HU (a) model (Davieset al., 1997), which relates the vertical eddy viscosity to the water depth and depth mean velocity, gives the closest results to the observed data. The reproduction of the amphidromic point of M₂ tide in Liaodong Bay is discussed and it is concluded that it depends on the bottom friction stress. The model reproduces a unique vertical profile of tidal current in the Yellow Sea, which is also found in the observed data. The reason for the reproduction of such a unique profile in the model is investigated.     

Modelling of the barotropic processes in the Bohai Sea

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Temperature variability caused by internal tides in the coastal waters of east coast of Peninsular Malaysia

The effects of tidal currents (i.e., barotropic and internal tides) are important in the biogeochemistry of a coastal shelf sea. The high-frequency of currents and near-bottom temperatures collected in three consecutive southwest monsoon seasons (May, June, July and August of 2013 until 2015) is presented to reveal the role of the tidal currents to the temperature variability in the coastal shelf sea of the east coast of Peninsular Malaysia (ECPM), south of the South China Sea (SCS). The results of a spectral density and harmonic analysis demonstrate that the near-bottom temperature variability and the tidal currents are influenced by diurnal (O₁ and K₁) and semidiurnal (M₂) tidal currents. The spectral density of residual currents (detided data) at 5, 10 and 16 m depth also shows significant peaks at the diurnal tidal frequency (K₁) and small peaks at the semidiurnal tidal frequency (M₂) indicating the existence of internal tides. The result of the horizontal kinetic energy (HKE) shows a strong intermittent energy of internal tides in the ECPM with the strongest energy is found at 16 m depth during a sporadic cooling event in June and July. A high horizontal cross-shore heat flux (16 m) also indicates strong intrusions of cooler water into the ECPM in June and July. During the short duration of cold pulse water observed in June and July, a cross-wavelet analysis also reveals the strong relationship between the near-bottom temperatures and the internal tidal currents at the diurnal tidal frequency. The intrusion of this cooler water is probably related to the monsoon-induced upwelling in June. It is loosely interpreted that the interaction between the strong barotropic tides and the steep slope in the central basin of the SCS under the stratified condition in southwest monsoon has generated these internal tides. The dissipation of internal tides from the slope area probably has driven the cold-upwelled water into the ECPM coastal shelf sea when the upwelling intensity is the highest in June and July.     

南海东沙岛西南大陆坡内潮特征

2008年4月-10月,在南海东沙岛西南大陆坡底部布放了1套全剖面锚系,同时沿大陆坡底部布放了3套近底锚系,应用谱分析和调和分析方法分析温度和海流连续观测资料,进而研究该海域的内潮特征.结果表明,东沙岛西南大陆坡存在强内潮现象,大陆坡底部温度变化受到内潮波的影响,上层海洋存在强日潮周期的内潮波振动;正压潮和斜压潮均以O...     

吕宋海峡M2内潮的三维数值模拟

A three-dimensional isopycnic-coordinate internal tidal model is employed to investigate the generation,propagation, vertical structure and energy conversion of M2 internal tides in the Luzon Strait(LS) with mooring observations. Simulated results, especially the tidal current amplitudes, agree well with observations,demonstrating the reasonability and accuracy of the model. Results indicate that M2 internal tides mainly propagate into three directions horizontally, i.e., eastward towards the western Pacific Ocean, westward towards the Dongsha Island and southwestward towards the South China Sea Basin. In the horizontal direction, tidal current amplitudes decrease as distance increases away from the LS; in the vertical direction, they show an obvious decreasing tendency with depth. Between the double ridges of the LS, a clockwise gyre of M2 baroclinic energy flux appears, which is caused by reflections of M2 internal tides at supercritical topographies, and resonance of M2 internal tides happens along 19.5° and 21.5°N due to the heights and separation distance of the double ridges. The total energy conversion in the LS is about 14.20 GW.     

Three-dimensional numerical model study of the residual current in the South China Sea

A three-dimensional baroclinic shelf sea model is employed to simulate the tidal and non-tidal residual current in the South China Sea. The four most significant constituents, M₂, S₂, K₁ and O₁, are included in the experiments with tidal effect. At most stations, the computed harmonic constants agree well with the observed ones. The circulations of the South China Sea in summer (August) and winter (December) are mainly discussed. It is shown that the barotropic tidal residual current is too weak to affect the South China Sea circulation, whilst the contribution of the baroclinic tidal residual current to the South China Sea circulation would be important in the continental shelf sea areas, especially in the Gulf of Thailand and Gulf of Tonkin. In the deep-sea areas, the upper barotropic or baroclinic tidal residual current is relatively very weak, however, the speed order of the deep baroclinic tidal residual current can be the same as that of the mean current without tidal effect. Moreover, the baroclinic tidal residual current seems to be related to the different seasonal stratification of ocean.     

Simulation of surface and internal semidiurnal tides in the Kara Sea

The problem of the dynamics of surface and internal waves M ₂ in the Kara Sea is solved within the QUODDY-4 3D finite-element hydrostatic model. It is shown that the conventional concept of surface-tide wave generation due to the interaction of two tidal waves (one arrives from the Barents Sea and the other is generated in the Arctic Ocean (AO) and propagates southward along the west coasts of Severnaya Zemlya) is only partially valid: the east branch of the tidal wave generated in the AO actually exists, but there is also a west branch that propagates along the St. Anna trough and another tidal wave that penetrates in the Kara Sea from the Laptev Sea through the Vilkitsky Strait. Simulated spatial distributions of the tidal velocities, amplitudes of internal tidal waves at the pycnocline depth, and some components of the budgets of barotropic and baroclinic tidal energy are discussed.     

南海北部陆架海域内潮特征的观测研究

利用2014年南海东沙岛西北部海域70余天的流速剖面高频观测资料,研究分析了该海区正压潮、内潮的时空分布特征。结果表明,观测海区正压潮流以O_1,K_1,M_2,S_2为主;斜压潮流中,除四大分潮之外,MU_2与2Q_1分潮能量也较强;内潮的主轴方向基本沿东南-西北方向,近似与局地等深线垂直。全日内潮的锁相部分占全日内潮能量的17.5%,而半日内潮的锁相部分占半日内潮能量的30%;进一步研究发现半日内潮主要由第一模态主导,而全日内潮第二模态占比50%,约为其第一模态能量的两倍;内潮模态能量占比显示出显著的大小潮调制的半月周期。对比不同垂向模态计算方法发现,当流速观测深度有限时,利用全水深温盐资料计算观测范围内流速垂向模态是更为准确的方式。     

Once again: once again—tidal friction

Topex/Poseidon (T/P) altimetry has reopened the problem of how tidal dissipation is to be allocated. There is now general agreement of a M₂ dissipation by 2.5 Terawatts (1 TW = 10¹² W), based on four quite separate astronomic observational programs. Allowing for the bodily tide dissipation of 0.1 TW leaves 2.4 TW for ocean dissipation. The traditional disposal sites since (1920) have been in the turbulent bottom boundary layer (BBL) of marginal seas, and the modern estimate of about 2.1 TW is in this tradition (but the distribution among the shallow seas has changed radically from time to time). Independent estimates of energy flux into the marginal seas are not in good agreement with the BBL estimates.T/P altimetry has contributed to the tidal problem in two important ways. The assimilation of global altimetry into Laplace tidal solutions has led to accurate representations of the global tides, as evidenced by the very close agreement between the astronomic measurements and the computed 2.4 TW working of the Moon on the global ocean. Second, the detection by and (1996) of small surface manifestation of internal tides radiating away from the Hawaiian chain has led to global estimates of 0.2 to 0.4 TW of conversion of surface tides to internal tides. Measurements of ocean microstructure yields 0.2 TW of global dissipation by pelagic turbulence (away from topography). We propose that pelagic turbulence is maintained by topographic scattering of barotropic into baroclinic tidal energy, via internal tides and internal waves. Previous estimates by (1974); , (1982)) of this conversion along 150,000 km of continental coastlines gave a negligible 0.02 TW; evidently the important conversion takes place along mid-ocean ridges.The maintenance of the abyssal global stratification requires a much larger expenditure of power. 2 TW versus 0.2 TW. This is usually attributed to wind forcing. If tidal power is to play a significant role here, then the BBL estimates need to be reduced. The challenge is to estimate dissipation from the energy flux divergence in the T/P adjusted tidal models, without prior assumptions concerning the dissipation processes.     

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.     

印度尼西亚海域潮波的数值研究

基于ROMS模式构建了模拟区域为(15.52°S-7.13°N,110.39°~134.15°E)水平分辨率为2′的潮波数值模式,分别模拟了印尼海域M2、S2、K1、O1四个主要分潮。模拟结果与29个卫星高度计交叠点上的调和常数进行比较,符合较好。M2分潮的振幅均方根差为3.4cm,迟角均方根差为5.9°;S2分潮的振幅均方根差为1.7cm,迟角均方根差为6.3°;K1分潮振幅均方根差为1.1cm,迟角均方根差为5.8°;O1分潮振幅均方根差为1.2cm,迟角均方根差为4.4°。M2、S2、K1、O1分潮向量均方根差分别为3.8cm、2.4cm、1.9cm和1.3cm,模拟结果的相对偏差在10%左右。根据计算结果分析了印尼海域的潮汐特征及潮能传播规律,结果显示:爪哇海以外的印尼海域主要为不规则半日潮区;全日潮潮能主要由太平洋传入印尼海域,而半日潮潮能则是从印度洋传入印尼海域。     

Non-assimilated tidal modeling of the South China Sea

The tides in the South China Sea were simulated using an established tidal model, with the purpose to evaluate if non-assimilated modeling of the area is feasible. Simulations were done for the locally dominating diurnal (K₁) and semi-diurnal (M₂) tidal constituents, and the model was shown to provide reasonably accurate results in terms of both elevations and levels of dissipation. However, this was only the case when a realistic tidal conversion parameterization was included in the model, and it is suggested that tidal conversion is a missing process in other model efforts of the area. Compared to observations, the modeled dissipation levels were slightly overestimated when integrated over the entire domain, and far larger in the model at topography with a slope which is supercritical for the baroclinic tidal waves. A crude, empirical correction of the tidal conversion rates at supercritical topography is suggested and implemented in the model and shown to improve the model results in terms of both elevations and dissipation rates. It is concluded that the presented model set up is suitable for investigations of how perturbations, e.g., future sea-level rise, will affect the tidal dynamics in the South China Sea.     

Ocean Tide Models Developed by Assimilating TOPEX/POSEIDON Altimeter Data into Hydrodynamical Model: A Global Model and a Regional Model around Japan

A global ocean tide model (NAO.99b model) representing major 16 constituents with a spatial resolution of 0.5° has been estimated by assimilating about 5 years of TOPEX/POSEIDON altimeter data into barotropic hydrodynamical model. The new solution is characterized by reduced errors in shallow waters compared to the other two models recently developed; CSR4.0 model (improved version of Eanes and Bettadpur, 1994) and GOT99.2b model (Ray, 1999), which are demonstrated in comparison with tide gauge data and collinear residual reduction test. This property mainly benefits from fine-scale along-track tidal analysis of TOPEX/POSEIDON data. A high-resolution (1/12°) regional ocean tide model around Japan (NAO.99Jb model) by assimilating both TOPEX/POSEIDON data and 219 coastal tide gauge data is also developed. A comparison with 80 independent coastal tide gauge data shows the better performance of NAO.99Jb model in the coastal region compared with the other global models. Tidal dissipation around Japan has been investigated for M₂ and K₁ constituents by using NAO.99Jb model. The result suggests that the tidal energy is mainly dissipated by bottom friction in localized area in shallow seas; the M₂ ocean tidal energy is mainly dissipated in the Yellow Sea and the East China Sea at the mean rate of 155 GW, while the K₁ energy is mainly dissipated in the Sea of Okhotsk at the mean rate of 89 GW. TOPEX/POSEIDON data, however, detects broadly distributed surface manifestation of M₂ internal tide, which observationally suggests that the tidal energy is also dissipated by the energy conversion into baroclinic tide.