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.     

Critical Latitude in Tidal Dynamics Using the Kara Sea as an Example

It is well known that, within the linear nonviscous equations of tidal dynamics, the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components unlimitedly increase when approaching the critical latitude. It is also known that the linear equations of tidal dynamics with a constant and specified vertical eddy viscosity indicate the occurrence of significant tidal velocity shears in the near-bottom layer, which are responsible for increasing the baroclinic tidal energy dissipation, the turbulent kinetic energy, and the thickness of the bottom boundary layer. The first circumstance—the growth of the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components—is due to the elimination in the original equations of small terms, which are small everywhere except for the critical latitude zone. The second circumstance—the occurrence of significant tidal velocity shears—is due to the fact that internal tidal waves, which induce the dissipation of the baroclinic tidal energy and the diapycnal diffusion, are either not taken into account or described inadequately. It is suggested that diapycnal diffusion can lead to the degeneration (complete or partial) of tidal velocity shears, with all the ensuing consequences. The aforesaid is confirmed by simulation results obtained using the QUODDY-4 high-resolution three-dimensional finite-element hydrostatic model along the 66.25° E section, which passes in the Kara Sea across the critical latitude.     

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…     

Tidal Mixing in the Kuril Straits and Its Impact on Ventilation in the North Pacific Ocean

A numerical study using a 3-D nonhydrostatic model has been applied to baroclinic processes generated by the K ₁ tidal flow in and around the Kuril Straits. The result shows that large-amplitude unsteady lee waves are generated and cause intense diapycnal mixing all along the Kuril Island Chain to levels of a maximum diapycnal diffusivity exceeding 10³ cm²s⁻¹. Significant water transformation by the vigorous mixing in shallow regions produces the distinct density and potential vorticity (PV) fronts along the Island Chain. The pinched-off eddies that arise and move away from the fronts have the ability to transport a large amount of mixed water (∼14 Sv) to the offshore regions, roughly half being directed to the North Pacific. These features are consistent with recent satellite imagery and in-situ observations, suggesting that diapycnal mixing within the vicinity of the Kuril Islands has a greater impact than was previously supposed on the Okhotsk Sea and the North Pacific. To examine this influence of tidal processes at the Kurils on circulations in the neighboring two basins, another numerical experiment was conducted using an ocean general circulation model with inclusion of tidal mixing along the islands, which gives a better representation of the Okhotsk Sea Mode Water than in the case without the tidal mixing. This is mainly attributed to the added effect of a significant upward salt flux into the surface layer due to tidal mixing in the Kuril Straits, which is subsequently transported to the interior region of the Okhotsk Sea. With a saline flux into the surface layer, cooling in winter in the northern part of the Okhotsk Sea can produce heavier water and thus enhance subduction, which is capable of reproducing a realistic Okhotsk Sea Mode Water. The associated low PV flux from the Kuril Straits to the open North Pacific excites the 2nd baroclinic-mode Kelvin and Rossby waves in addition to the 1st mode. Interestingly, the meridional overturning in the North Pacific is strengthened as a result of the dynamical adjustment caused by these waves, leading to a more realistic reproduction of the North Pacific Intermediate Water (NPIW) than in the case without tidal mixing. Accordingly, the joint effect of tidally-induced transport and transformation dominating in the Kuril Straits and subsequent eddy-transport is considered to play an important role in the ventilation of both the Okhotsk Sea and the North Pacific Ocean. This revised version was published online in July 2006 with corrections to the Cover Date.     

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).     

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.     

Diapycnal mixing by meso-scale eddies

The mean available potential energy released by baroclinic instability into the meso-scale eddy field has to be dissipated in some way and Tandon and Garrett [Tandon, A., Garrett, C., 1996. On a recent parameterization of mesoscale eddies. J. Phys. Oceanogr. 26 (3), 406–416] suggested that this dissipation could ultimately involve irreversible mixing of buoyancy by molecular processes at the small-scale end of the turbulence cascade. We revisit this idea and argue that the presence of dissipation within the thermocline automatically requires that a component of the eddy flux associated with meso-scale eddies must be associated with irreversible mixing of buoyancy within the thermocline. We offer a parameterisation of the implied diapycnal diffusivity based on (i) the dissipation rate for eddy kinetic energy given by the meso-scale eddy closure of Eden and Greatbatch [Eden, C., Greatbatch, R.J., 2008. Towards a meso-scale eddy closure. Ocean Modell. 20, 223–239.] and (ii) a fixed mixing efficiency. The implied eddy-induced diapycnal diffusivity (κ) is implemented in a coarse resolution model of the North Atlantic. In contrast to the vertical diffusivity given by a standard vertical mixing scheme, large lateral inhomogeneities can be found for κ in the interior of the ocean. In general, κ is large, i.e. up to o(10) cm²/s, near the western boundaries and almost vanishing in the interior of the ocean.     

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。     

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.     

Energetics of wind-induced turbulent mixing in the ocean

The pattern and magnitude of the global ocean overturning circulation is believed to be strongly controlled by the distribution of diapycnal diffusivity below 1000 m depth. Although wind stress fluctuation is a candidate for the major energy sources of diapycnal mixing processes, the global distribution of wind-induced diapycnal diffusivity is still uncertain. It has been believed that internal waves generated by wind stress fluctuations at middle and high latitudes propagate equatorward until their frequency is twice the local inertial frequency and break down via parametric subharmonic instabilities, causing diapycnal mixing. In order to check the proposed scenario, we use a vertically two-dimensional primitive equation model to examine the spatial distribution of “mixing hotspots” caused by wind stress fluctuations. It is shown that most of the wind-induced energy fed into the ocean interior is dissipated within the top 1000 m depth in the wind-forced area and the energy dissipation rate at low latitudes is very small. Consequently, the energy supplied to diapycnal mixing processes below 1000 m depth falls short of the level required to sustain the global ocean overturning circulation.     

Numerical Study on Tidal Mixing in the Bohai Sea

The spatial and temporal variability of tidal mixing in Bohai Sea is studied using a numerical approach. In calculating tidal mixing, accurate barotropic tidal current is obtained via a harmonic analysis package utilizing the simulated current output from a high-resolution regional ocean model. And a “small-scale” roughness map is adopted to describe the detailed topographic features of Bohai Sea. It is shown that the tidal mixing estimated in Bohai Sea is much higher than the level of global background, and fluctuates considerably at some regions within a single day. In Liaodong Bay, Bohai Bay and Bohai Strait, the mixing varies greatly, with the peak value of O (10^?2) m² s^?1. The order of magnitude of mixing in Laizhou Bay is about O (10^?5～10^?3) m² s^?1. Mixing with background level of O (10^?5) m² s^?1 only appears in central area. Result also shows that rough topography plays relatively a more important role than tidal current in enhancing diapycnal mixing in Bohai Sea. The distributions of tidal mixing in selected sections reveal that the vertical stratification in Bohai Sea is not obvious, generally renders a barotropic structure.     

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.     

The structure of the tidal mixing front in the region of Shantar Islands (Sea of Okhotsk) according to data of satellite observations

The location and seasonal variability of the tidal mixing front in the region of Shantar Islands are studied based on an analysis of satellite data. The Shantar tidal mixing front is related to the main features of the oceanographic structure of the northwestern shelf of the Sea of Okhotsk in summer. This front separates the coastal waters mixed by tidal currents and the stratified part of the shelf. The temperature tidal mixing front forms in July after the melting ice cover and disappears in the end of October when the stratification is broken. The mean position of the front changes insignificantly and is determined by the critical value of the Simpson-Hunter parameter (logh/u ₃ = 2.5); the front is located over the isobath of 50 m. The temperature tidal mixing front corresponds to the front in the distribution of chlorophyll a determined from SeaWiFS and MODIS satellite imagery. High (when compared to the stratified part of the shelf) concentrations of chlorophyll a were observed within the zone of intense tidal mixing. Satellite images in the IR range of the spectrum (Landsat-5 TM) demonstrated that the front is dynamically unstable. Mixing effects connected with frontal submesoscale baroclinic eddies have an influence on the structure of the stratified part of the shelf.     

Modified parameterization for near-inertial waves

The near-inertial waves (NIWs) are important for energy cascade in the ocean. They are usually significantly reinforced by strong winds, such as typhoon. Due to relatively coarse resolutions in contemporary climate models, NIWs and associated ocean mixing need to be parameterized. In this study, a parameterization for NIWs proposed by Jochum in 2013 (J13 scheme), which has been widely used, is compared with the observations in the South China Sea, and the observations are treated as model outputs. Under normal conditions, the J13 scheme performs well. However, there are noticeable discrepancies between the J13 scheme and observations during typhoon. During Typhoon Kalmaegi in 2014, the inferred value of the boundary layer is deeper in the J13 scheme due to the weak near-inertial velocity shear in the vertical. After typhoon, the spreading of NIWs beneath the upper boundary layer is much faster than the theoretical prediction of inertial gravity waves, and this fast process is not rendered well by the J13 scheme. In addition, below the boundary layer, NIWs and associated diapycnal mixing last longer than the direct impacts of typhoon on the sea surface. Since the energy dissipation and diapycnal mixing below the boundary layer are bounded to the surface winds in the J13 scheme, the prolonged influences of typhoon via NIWs in the ocean interior are missing in this scheme. Based on current examination, modifications to the J13 scheme are proposed, and the modified version can reduce the discrepancies in the temporal and vertical structures of diapycnal mixing.     

吕宋海峡及周边海域湍流混合的时空分布特征研究

利用1992—2002年的温盐深数据与2012—2016年的Argo数据,基于细尺度参数化方法研究了吕宋海峡及周边海域(12°—30°N,115°—129°E)湍流混合的时空分布特征,并分析了地形粗糙度、内潮以及风输入的近惯性能通量对湍流混合的影响。结果表明,吕宋海峡和东海陆坡处具有强混合的特征,扩散率高达4×10~(-3) m~2/s,主要是由内潮产生导致的,其中吕宋海峡主要是M2、K1和O1内潮的贡献,而东海陆坡处主要是M_2内潮的贡献;南海北部也呈现较强的混合,且陆坡处的混合比海盆高1—2个量级;南海中央海盆和离岸的菲律宾海混合较弱,扩散率为O (10-5 m2/s)。此外,在研究区域内,湍流混合的年际变化和季节变化均不明显,且混合扩散率与风输入的近惯性能通量未表现出明显的季节相关。     

Numerical study of tide-induced mixing over rough bathymetry in the abyssal ocean

Locally enhanced turbulent mixing over rough bottom bathymetry is one of the candidates that might make up for the lack of diapycnal diffusivity in maintaining the global overturning circulation. In the present study, using a two-dimensional vertical numerical model for the Brazil Basin, we numerically examine the intensity and vertical structure of tide-induced mixing over multi-beam bottom bathymetry via the comparison with those over somewhat smoothed bottom bathymetry. Note that even this smoothed bottom bathymetry is finer than in commonly used datasets. In comparison to the response over the smoothed bottom bathymetry, energy dissipation rates are enhanced within a few hundred meters over the multi-beam bottom bathymetry. In spite of several limitations of the two-dimensional vertical numerical model, the magnitude and vertical distribution of the calculated dissipation rates agree well with those from microstructure measurements. We find that tidal interaction with fine-scale (≤2 km) bottom bathymetry efficiently generates high wavenumber internal waves, which are subject to local energy dissipation and hence strongly control the abyssal mixing; the most important finding is that the intensity and vertical decay scale of abyssal mixing are in a trade-off relationship with each other, which is not taken into account in the existing parameterizations.     

一个考虑潮汐、中尺度涡和地形影响的南海底部环流诊断模型

本文构造了一个考虑潮汐、中尺度涡和地形影响下的南海底部环流诊断模型。在该模型中,潮汐混合和涡致混合引起的垂直速率用一个类似的改进参数化方案来表示。该模型结果显示在南海深层吕宋海峡"深水瀑布"和斜压影响最大,潮汐作用和中尺度涡影响次之,风场的影响最小。斜压影响的整体效应与其他因素相反。潮汐混合与涡致混合具有明显的地形依赖性。潮汐混合主要集中在南海北部海盆地形较为陡峭的陆坡区和南海中部海山区,而涡致混合主要集中在海盆西边界区以及中部海山区。在不考虑吕宋海峡"深水瀑布"、潮汐和中尺度涡的情况下(对应吕宋海峡关闭),南海底部环流为反气旋式环流。考虑吕宋海峡"深水瀑布"后,南海底层环流为气旋式环流,而潮汐混合和涡致混合起到加强整个气旋式环流强度的作用。此外,该模型还给出了南海底部环流量级大小与地形坡度之间的密切关系,即地形坡度较大的地方,其流速也大。这对于现场观测有着一定的参考意义。最后,本文用尺度分析的方法从理论上分析了该模型的适用性,证实了该模型具有一定的可靠性。     

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。     

南海北部中深层细结构混合研究

基于2007年8月获得的ADCP（声学多普勒流速剖面仪）海流资料和CTD（温盐深剖面仪）水文资料，应用Gregg模型对南海中深层内波尺度的混合进行估计，同时应用Thorpe尺度对中深层存在的垂向翻转及由此引起的混合进一步分析。两种方法均显示，吕宋海峡附近上层400m的耗散率及混合率均强于18&#176;N断面，中深层两个区域的混合率并没有显著区别。这表明吕宋海峡上层400m，可能存在更活跃的内波活动，从而产生更强的内波混合和垂向水团翻转。Gregg模型估计的耗散率和混合率量级分别为10^-9W&#183;kg^-1和10^-6m^2&#183;s^-1。大部分CTD站位在中深层均存在垂向翻转，而且保持较高的发生率，翻转所对应的混合率并不随深度增加而减小。以上南海北部的细结构混合特征增强对南海中深层混合的认识。     

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.