On diapycnal mixing induced by internal tidal waves in the Arctic Ocean

In order to reproduce the diapycnal mixing induced by internal tidal waves (ITWs) in the Arctic Ocean, we use a modified version of the three-dimensional finite-element hydrothermodynamic model QUODDY-4. We found that the average (over the tidal cycle) and integral (by depth) baroclinic tidal energy dissipation rate in individual areas of the Siberian continental shelf and in the straits between the Canadian Arctic archipelago are much higher than in the open ocean and its values on ridges and troughs are qualitatively similar to one another. Moreover, in the area of open-ocean ridges, the baroclinic tidal energy dissipation rate increases as it approaches the bottom, but only in the bottom boundary layer; on the Mid-Atlantic and Hawaii ridges, such an increase is observed within a few hundreds of meters away from the bottom. The average (in area and depth of the open ocean) coefficient of diapycnal mixing defined by the baroclinic tidal energy dissipation rate is higher than the coefficient of molecular kinematic viscosity and only a few times lower than the canonical value of the coefficient of vertical turbulent viscosity, which is used in models of global oceanic circulation. Coupled with the reasoning on the localization of baroclinic tidal energy dissipation, this fact leads to the conclusion that disregarding the contribution that ITW-induced diapycnal mixing makes to the ocean-climate formation is hardly justified.     

Dissipation of baroclinic tidal energy and diapycnal mixing in the White Sea

The modeling results obtained using the original version of the three-dimensional finite-element hydrostatic model QUODDY-4 testify that the spatial distributions of dissipation of baroclinic tidal energy and the related coefficient of diapycnal mixing in the deepwater stratified subdomain of the White Sea (the Basin and Kandalaksha and Dvina bays together) are highly similar to those found for low- and midlatitude oceans. It is in the open part of the sea that their values remain equal to the minimum possible values determined by the molecular kinematic viscosity; at its lateral boundaries (not all boundaries, but only individual segments (sites of mixing)), their values increase. In the shallow homogeneous subdomain of the White Sea, the dissipation of baroclinic tidal energy is considerably larger than in the deep stratified subdomain. Accordingly, the vertical eddy viscosity in the first subdomain is a few orders of magnitude higher than the coefficient of diapycnal mixing in the second subdomain. This is caused by an increased tidal velocity due to reduced depths.     

Estimates of mixing on the South China Sea shelf

1 Introduction The outer shelf of the South China Sea is a di- verse environment characterized by sharp changes in bottom topography (Wang et al., 2002). Internal wave and diapycnal mixing may be a vital mechanism con- trolling the distribution of physical water properties, nutrient fluxes, and concentrations of particulate mat- ter. Therefore, the research on diapycnal mixing on the outer shelf in the South China Sea is of great impor- tance to explore the level and variability of the abov…     

Influence of the White Sea on tides in adjacent marginal seas of the North European Basin

An investigation into the interaction of surface M ₂ tides in the system of marginal seas of the North European Basin is carried out using the three-dimensional finite-element hydrostatic model QUODDY-4. Three numerical experiments are performed for this purpose. In the first (control), the model equations are solved in the system of the Norwegian, Greenland, Barents, and White seas; thereby the interaction of the tides in these seas is explicitly taken into account. In the second experiment, the White Sea is excluded from consideration and the no-flux condition is posed at the entrance to the sea. The third experiment uses an approach in which the observed tidal elevations that determine the existence of a finite horizontal transport of barotropic energy to the White Sea are specified at the open boundary of the White Sea. It is shown that changes in tidal dynamics represented by changes in the amplitudes and phases of tidal elevations and in the barotropic tidal velocity ellipse parameters are within the model noise in experiments 2 and 3 when compared with the control experiment. On the contrary, changes in energy characteristics (the horizontal wave transport, density, and dissipation rate of barotropic tidal energy) are equal to or greater (in order of magnitude) than the energy characteristics themselves.     

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.     

南海吕宋海峡21°N附近多潜标观测的上层海流

为了了解潮流从西北太平洋经吕宋海峡进入南海内的变化及其垂向结构,本文利用在吕宋海峡附近沿东西方向布放的多套潜标同步获得的高分辨率ADCP长时间连续观测上层海流资料,使用调和分析方法将实测海流分解成3部分:不随时间变化的定常流、周期性潮流和剩余流,并将潮流分解为正压潮流和斜压潮流。通过对实测海流中各组分的分析,得到以下结论:该区域潮流类型在不同深度上有明显变化;M2潮自吕宋海峡传入南海后强度显著减弱75%左右,K1、O1分潮在上层强度减弱约三分之一。从垂向变化来看,在潮流强度上,各站点垂直方向上潮流强度均发生变化。从方向上看,各分潮潮流椭圆东西向特征明显,长轴变化较大,短轴(南北向特征)垂向变化不显著;潮流运动主要沿逆时针方向,垂直方向上潮流明显减弱或增强时会发生转向。斜压潮流主要集中在上表层,100m左右以下随深度逐渐减弱。东西方向斜压潮流能量比正压潮流强,而南北向的流比较稳定,且斜压潮流能量远小于正压潮流。定常流强度在各站点呈现相似的变化趋势,随深度变化减弱。     

Internal tide generation by seamounts

The generation of internal tidal wave fields by barotropic tidal flow past a representative seamount is computed by modelling the seamount as a pillbox, and linearising the equations for internal wave dynamics. This is justifiable for mid-ocean seamounts, which constitute steep topography for internal waves of tidal frequency. For linearly polarised barotropic tidal flow, the resulting flow field consists of conical beams radiating from the region above the seamount, with largest velocities aligned with the barotropic flow. These beams vary with azimuthal angle but resemble the corresponding beams from two-dimensional steep topography, particularly in the barotropic flow direction. They are primarily forced by the barotropic flow over the seamount, which is amplified by the topography and is independent of the stratification if the radius of the seamount is sufficiently large. In a barotropic tidal flow of 1 cm/s amplitude, energy fluxes from individual seamounts are of order 10⁶ W. Summing this over all seamounts higher than 1 km gives baroclinic energy generation of order 5.10⁹ W, a number that is less than estimates of baroclinic energy flux from the continental slopes and the Hawaiian ridge, but is comparable with them.     

Verification studies for a z-coordinate primitive-equation model: Tidal conversion at a mid-ocean ridge

We document the accuracy and convergence of solutions for a z-coordinate primitive-equation model of internal tide generation and propagation. The model, which is based on MOM3 numerics, is linearized around a state of rest to facilitate comparison with analytic estimates of baroclinic generation at finite-amplitude topography in a channel forced by barotropic tidal flow at its boundaries. Unlike the analytical model, the numerical model includes mixing of both buoyancy and momentum, and several definitions of “baroclinic conversion” are possible. These are clarified by writing out the energetics of the linearized equations in terms of barotropic kinetic energy, baroclinic kinetic energy, and available potential energy. The tidal conversion computed from the model, defined as the rate of conversion of barotropic kinetic energy into available potential energy, agrees well with analytical predictions. A comparison of different treatments of bottom topography (full-cells, partial-cells, and ghost-cells) indicates that the partial-cell treatment is the most accurate in this application. Convergence studies of flow over a smooth supercritical ridge show that the dissipation along tidal characteristics is, apparently, an integrable singularity. When the ocean bottom is not smooth, the accuracy and convergence of the model depend on the power spectrum of the topography. A numerical experiment suggests that the power spectrum of the resolved topography must roll off faster than k⁻² to obtain convergent results from a linear numerical model of this type.     

Seasonal variability of surface and internal M<Subscript>2</Subscript> tides in the Arctic Ocean

The modeling results of surface and internal M₂ tides for summer and winter periods in the Arctic Ocean (AO) are presented. We employed a modified version of the three-dimensional finite-element hydrothermodynamic model QUODDY-4 differing from the original model by using a rotated (instead of spherical) coordinate system and by considering the equilibrium-tide effects. It has been shown that the modeling results for the surface tide differs little from the results obtained earlier by other authors. According to these results, the amplitudes of internal tidal waves (ITWs) in the AO are significantly lower than in other oceans and the ITWs proper have the character of trapped waves. Their source of generation is located at the continental slope northwest of the New Siberian Islands. Our results are consistent with the fields of average (over a tidal cycle) and integral (by depth) densities of baroclinic tidal energy, the maximum baroclinic tidal velocity, and the coefficient of diapycnic mixing. The local rate of baroclinic tidal energy dissipation at the AO ridges increases as it approaches the bottom, as was observed on Mid-Atlantic and Hawaii ridges (but merely within the bottom boundary layer) and is two to three orders of magnitude lower than in other oceans. The ITW degeneration scale in the AO is several hundreds of kilometers in summer and winter, remaining within the range of its values between 100 and 1000 km in mid- and low-latitude oceans. In both seasons, the integral (over the AO area) rate of baroclinic tidal energy dissipation is two orders of magnitude lower than the global estimate (2.5 × 10¹² W).     

南海西北陆坡区内潮与近惯性内波观测研究

通过对2006年南海西北部海域近3个月的全水深流速观测资料的分析,研究了该海区正压潮、内潮及近惯性内波的时空分布特征。结果表明,全日内潮明显强于半日内潮,且最大潮流均出现在海洋上层;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;内潮能量显示出明显的时间长度约为半月的大小潮调制周期;全日内潮的coherent部分占全日内潮能量的70%,而半日内潮的coherent部分占半日内潮能量的53%;进一步研究发现半日内潮主要由第一模态主导,而全日内潮第三模态能量占总能量的比例仅次于第一模态且量值上与之相当;强风过程可激发出强的近惯性运动,暖涡使得近惯性内波能量更有效地向海洋深层传播,冷涡则不利于近惯性内波能量向下传播。     

南海北部东沙岛附近的内潮和余流特征

采用东沙岛附近的一个长达9个月的锚定潜标的观测资料对南海北部的正压潮、内潮和余流情况进行了分析,得到了当地正压潮和内潮的特征。此处正压潮流以全日潮为主,秋、冬季相对较大,春季相对较小;正压余流受海盆尺度环流和地形的限制,在潜标观测期间的秋、冬、春三季基本以偏西向的正压流为主。内潮同正压潮一样,也以全日分潮为主,潮流椭圆随水深发生旋转,在110—120m附近存在内潮非常弱的一层。斜压余流在2009年2—3月比较异常,这是由于在此其间有一个中尺度涡经过。对此潜标数据采用经验正交函数分解的方法进行分析,发现海流的各个主要EOF模态与内波的垂向模态结构有一定的关联。     

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.     

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。     

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.     

An abyssal recipe

Fine- and microstructure observations indicate bottom-intensified turbulent dissipation above rough bathymetry associated with internal wave breaking. Simple analytic representations for the depth profile of turbulent dissipation are proposed here under the assumption that the near bottom wavefield is dominated by a baroclinic tide. This scheme is intended for use in numerical models and thus captures only the gross features of detailed solutions to the energy balance of the internal wavefield. The possible sensitivity of the magnitude and vertical variability of the dissipation rate profile to various environmental parameters is discussed. An expression for the diapycnal buoyancy flux is presented that explicitly treats the difference between the height of an isopycnal above the mean bottom and the actual bottom. This returns a diapycnal velocity estimate that is consistent with both tracer observations of downwelling and a basin scale mass budget that requires upwelling.     

An abyssal recipe

Fine- and microstructure observations indicate bottom-intensified turbulent dissipation above rough bathymetry associated with internal wave breaking. Simple analytic representations for the depth profile of turbulent dissipation are proposed here under the assumption that the near bottom wavefield is dominated by a baroclinic tide. This scheme is intended for use in numerical models and thus captures only the gross features of detailed solutions to the energy balance of the internal wavefield. The possible sensitivity of the magnitude and vertical variability of the dissipation rate profile to various environmental parameters is discussed. An expression for the diapycnal buoyancy flux is presented that explicitly treats the difference between the height of an isopycnal above the mean bottom and the actual bottom. This returns a diapycnal velocity estimate that is consistent with both tracer observations of downwelling and a basin scale mass budget that requires upwelling.     

A method of accounting for tidal changes in regional climates of a water basin under conditions of an ice-free Barents Sea

To account for tidal variations in the regional climate of a water basin, we propose adding up the vertical eddy diffusivity, determined by wind and thermohaline forcings, and the diapycnal diffusivity, determined from the solution to the problem of the internal tidal wave (ITW) dynamics. This approach agrees with the approximation of “weak interaction” between turbulence of various origins. Then, the hydrothermodynamics equations are integrated with and without regard for ITW-induced diapycnal diffusion until a quasistationary solution is reached. Next we compare these solutions, found by using the 3D finite-element hydrostatic model QUODDY-4. This comparison shows that the contribution of tides to the formation of the Barents Sea climate in summer is not negligible with respect to certain hydrological characteristics. We present the fields of the dynamic topography of a free surface, surface current velocities, and seawater temperature and salinity at the depth of the pycnocline in the sea to illustrate the occurrence of tidal effects.     

莫桑比克海峡及其邻近海区正压潮流数值模拟与能量收支分析*

莫桑比克海峡及其邻近海区是全球海洋潮流和潮能耗散最强的海区之一。文章利用高分辨率通用环流模式对该海区的正压潮流进行模拟, 并对该海区潮能通量和潮能耗散特征进行分析。结果表明, 莫桑比克海峡及其邻近海区的潮波主要是半日分潮占主导地位, 全日分潮可忽略不计, M₂分潮形成1个左旋潮波系统和1个右旋潮波系统, S₂分潮形成1个左旋潮波系统。莫桑比克海峡和马达加斯加岛南部等绝大数区域的M₂和S₂半日潮流是逆时针旋转, 在马达加斯加岛顶部等局部区域是顺时针旋转, 而且在海峡通道等复杂地形处潮流流速量级较大。潮能通量矢量主要来自东边界, 大部分潮能通量沿马达加斯岛北部传入莫桑比克海峡区域, 其中经过马达加斯加岛北部和进入莫桑比克海峡的M₂ (S₂)分潮的潮能通量分别为156.86GW (40.53GW)和148.07GW (36.05GW), S₂分潮潮能通量的量级大约为M₂分潮的1/5~1/4。底摩擦耗散主要发生莫桑比克海峡和马达加斯加岛南北部, 其中莫桑比克海峡M₂ (S₂)分潮的底摩擦耗散为1.762GW (0.460GW), 占其底部总耗散的43.74% (39.72%)。     

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...     

Numerical model of nonhydrostatic ocean dynamics based on methods of artificial compressibility and multicomponent splitting

An algorithm is proposed for solving three-dimensional ocean hydrodynamics equations without hydrostatic approximation and traditional simplification of Coriolis acceleration. It is based on multicomponent splitting of the modified model with artificial compressibility. The original system of equations is split into two subsystems describing the transport of three velocity components and adjustment of the density and velocity fields. At the adjustment stage, the horizontal velocity components are represented as a sum of the depth means and deviations; the two corresponding subsystems are derived. For barotropic dynamics, the compressibility effect is represented as the boundary condition at the free surface, while for the baroclinic subsystem, it is introduced as ε-regularization of the continuity equation. Then, the baroclinic equations are split into two subsystems describing the hydrostatic and nonhydrostatic dynamics. The nonhydrostatic dynamics is computed at a separate splitting stage. The algorithm is included into the Institute of Numerical Mathematics of the Russian Academy of Sciences model based on “primitive” equations and verified by solving the hydrodynamics problem for the Sea of Marmara.