A hydraulic experiment on tidal exchange

Tidal exchange through a narrow entrance channel was studied experimentally with the use of a simplified hydraulic model. The inflowing water mass, visualized with dye solution, exhibits the shape of a starting plume with a starting vortex pair at its head. Because of their periodical formation by the tide, these are called the tidal plume and tidal vortex pair. The axis of the tidal plume deflects and undulates with a period 2 to 9 times that of the tide. Together with this undulation, the vortex pair becomes asymmetric. A circulating flow is formed in the bay which affects the shape of the inflowing and outflowing water masses. A part of the inflowing water mass flows out during the subsequent ebb, and this outflowing portion can be divided into two parts. One is the water remaining in the entrance channel at high water which flows out during the first half of the subsequent ebb and the other is the water flowing round the bay in the circulating flow during flood that flows out during the latter half of the subsequent ebb. Both contribute to the exchange ratio, but we can estimate an upper limit for the exchange ratio by neglecting the latter outflow. This neglected portion is considered in the concept of the age composition of outflowing water. The age composition of the bay water shows the existence of intermittent effluence superposed on a trend in the age composition that is similar to that of the well-mixed case. From the analysis of a model consisting of a number of mixing tanks connected in series with a recycle flow, it is concluded that this intermittent effluence occurs in the case of weak mixing due to the effect of circulating flow in the bay but is negligible in the case of strong mixing.     

Bashi channel,Luzon strait: A hydraulic model experiment of the tidal current

Bottom current conditions due to tidal currents in the area of the Bashi Channel, Luzon Strait, are examined using a scaled hydraulic model in a uni-directional flow channel. The geometrical model is scaled in both the similitude of Froude's Number and the similitude of the four-thirds power law of eddy viscosity. The currents obtained from the experiment seem to be consistent in order of magnitude with the estimated currents based on observations made by Offshore Environmental System Ltd. In a quasi-steady tidal phase, formation of a strong core flow is found in the Bashi Channel. It can be explained by a simple theoretical model in which the formation of the strong current is attributed to the submarine topography of the Luzon Strait.     

Effect of boundary geometries on tidal currents and tidal mixing

The effects of the coastal boundary geometries on the tidal currents and the tidal mixing are studied mainly on the basis of hydraulic model experiments. Mizushima-Nada Sea, which is located in the central part of Seto Inland Sea, and the whole Seto Inland Sea were chosen as the prototypes.Currents and eddies geometrically induced in the tidal currents and in the ocean currents have significant effects on the water exchange, from small scales to meso scales, in the bays and near-shore regions of the ocean.As to small scale phenomena near irregular coastal boundaries such as river mouths, headlands and harbors, tidal currents produce organized eddy currents of the width scale. They are important to the temporary flushing and the local redistribution of the river water or the waste water.As to phenomena of larger scales, the tidal currents produce rather steady residual circulations in each part of the Inland Sea, due to the non-linear effects of the oscillating component. They are controlled by the geometry of the sea as separated by a narrow strait. These horizontal circulations of about 20 km in scale become the main mechanism of the water exchange in the Inland Sea. The one-dimensional dispersion coefficient due to these circulations is proportional to the product of the diameter and the current velocity of the circulations. The proportional constant takes the value of 0.40.5.     

Structure of tidal mixing at the Hayasui Straits

Based on the observation at the Hayasui Straits, actual conditions of the tidal mixing, of two water masses separated by the strait, are investigated for the time scale shorter than the the tidal period. Analyses show that the tidal mixing of water masses occurs by the disintegration of mutually penetrating small masses of water, which have been produced by the reciprocating tidal motion of the water masses with some topographical effect, especially at the slack water as large tongues. The mutual penetration occurs rather horizontally, and some of these turbulent smaller masses of water keep their own properties for a rather long period of the order of three hours, without mixing even in the violent shear flows. Initial horizontal scale of these turbulent masses is estimated as of the order of three kilometers. These actual conditions reveal themselves as the macroscopic diffusion coefficient.     

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。     

基于Delft 3D模型的感潮河口示踪模拟

为研究感潮河口的水力特征及溶质扩散规律,通过布放仪器监测水文参数,分析研究区的水力特征;采用荧光染色剂罗丹明B作为示踪剂开展现场示踪实验,研究示踪剂的扩散规律;基于Delft 3D模型的水动力模块与示踪模块相耦合,对研究区的动力场和示踪结果进行模拟,获取了小清河口的水平湍流扩散系数。结果表明:调查期间(非汛期)小清河口的水力条件主要受潮汐控制,潮汐对河口下游的作用更明显。由于河流径流量较小,在潮汐作用下,示踪剂从小清河口向海传输的速度较慢,导致示踪剂在河口长时间滞留。相关性分析(R²)和均方根误差(RMSE)结果表明示踪剂迁移模拟结果的可靠性高。基于本研究得到小清河口的水平湍流扩散系数(D_ξ,η)为6t^0.12m²/s。本研究可为小清河口以及同类河口中水平湍流扩散系数的估值提供参考,对于评价污染物在同类河口中的传输行为具有指导意义。     

Barotropic tidal mixing effects in a coupled climate model: Oceanic conditions in the Northern Atlantic

Impacts of mixing driven by barotropic tides in a coupled climate model are investigated by using an atmosphere–ocean–ice–land coupled climate model, the GFDL CM2.0. We focus on oceanic conditions of the Northern Atlantic. Barotropic tidal mixing effects increase the surface salinity and density in the Northern Atlantic and decrease the RMS error of the model surface salinity and temperature fields related to the observational data.     

Numerical simulation of tidal bores and hydraulic jumps

An implicit finite difference formulation of the nonlinear shallow water equations is developed to allow for the treatment of tidal bores and hydraulic jumps. Five different schemes are investigated involving upwind treatment of convective terms, central differences combined with dissipative interface, forward time-centering and various combinations of these techniques. The schemes are analyzed with respect to their effective amplification portraits, and they are tested on periodic bores, uniform bores and steady hydraulic jumps. In this connection the model results are verified against analytical solutions and a numerical solution obtained with a Godunov Riemann solver. Scheme 4, which combines forward time centering and dissipative interface, is found to be superior to the others and it is applicable for Courant numbers within the range 0.25 to 1.5. This scheme is applied to a case study of the tidal bore in Huangzhou Bay and Qiantang River. The model results are shown to be in very good agreement with field data.     

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.     

Response of a climate model to tidal mixing parameterization under present day and last glacial maximum conditions

Experiments with a climate model were conducted under present day and last glacial maximum conditions in order to examine the model’s response to a vertical mixing scheme based on internal tide energy dissipation. The increase in internal tide energy flux caused by a 120 m reduction in sea level had the expected effect on diffusivity values, which were higher under lower sea level conditions. The impact of this vertical diffusivity change on the Atlantic meridional overturning is not straightforward and no clear relationship between diffusivity and overturning is found. There exists a weak positive correlation between overturning and changes to the power consumed by vertical mixing. Most of the climatic response generated by sea level change was not related to alterations in the internal tide energy flux but rather to the direct change in sea level itself.     

渤海的潮混合特征及潮汐锋现象

人们对黄海的潮汐锋现象已有一些报道和研究[1～4],但对渤海的潮汐锋现象却没有进行过认真的分析和讨论,迄今只有赵保仁[1]在讨论黄海的潮汐锋时,指出过渤海海峡的潮汐锋现象;而黄大吉等[5]在数值计算渤海的温度变化时也指出在渤海内部存在着潮汐锋现象,但却没有进行深入的分析和给出任何实测证据.本文试图根据方国洪和曹德明最近在渤海取得的潮汐潮流数值计算结果1),计算由Simpson等[6]提出的陆架海的潮混合层化参量,来讨论渤海的潮混合特征;并进一步利用实测水文资料和海面温度的卫星遥感图像来说明渤海潮汐锋的分布和变化特征.     

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.     

一个东海潮汐数值模式及检验

为验证一个东海潮汐数值模式结果的精度并了解我国东海区域的潮汐特征。该文使用T_TIDE对东海大桥南和洋山站的潮汐资料进行调和分析, 并针对所研究区域最主要的8个分潮: M₂、S₂、K₁、O₁、N₂、K₂、P₁、Q₁分别对比两站实测数据与模式结果的调和分析结果。结果表明: 两站点的模式结果和观测海表高度的均方误差D与潮汐产生的海表高度变化V的比值为25.99%和25.29%, 模式结果计算所绘制的M₂和K₁分潮的同潮图与前人研究结果在无潮点的位置、同潮时线、等振幅线的分布和趋势上相似。这说明了使用时间长度相同但年份不同的实测数据验证潮汐数值模式结果的可行性, 并能够帮助了解我国东海区域的潮汐特征。     

Abyssal recipes II: energetics of tidal and wind mixing

Without deep mixing, the ocean would turn, within a few thousand years, into a stagnant pool of cold salty water with equilibrium maintained locally by near-surface mixing and with very weak convectively driven surface-intensified circulation. (This result follows from Sandström’s theorem for a fluid heated and cooled at the surface.) In this context we revisit the 1966 “Abyssal Recipes”, which called for a diapycnal diffusivity of 10^-4m²/s (1 cgs) to maintain the abyssal stratification against global upwelling associated with 25 Sverdrups of deep water formation. Subsequent microstructure measurements gave a pelagic diffusivity (away from topography) of 10^-5 m²/s — a low value confirmed by dye release experiments.A new solution (without restriction to constant coefficients) leads to approximately the same values of global upwelling and diffusivity, but we reinterpret the computed diffusivity as a surrogate for a small number of concentrated sources of buoyancy flux (regions of intense mixing) from which the water masses (but not the turbulence) are exported into the ocean interior. Using the Levitus climatology we find that 2.1 TW (terawatts) are required to maintain the global abyssal density distribution against 30 Sverdrups of deep water formation.The winds and tides are the only possible source of mechanical energy to drive the interior mixing. Tidal dissipation is known from astronomy to equal 3.7 TW (2.50±0.05 TW from M₂ alone), but nearly all of this has traditionally been allocated to dissipation in the turbulent bottom boundary layers of marginal seas. However, two recent TOPEX/POSEIDON altimetric estimates combined with dynamical models suggest that 0.6–0.9 TW may be available for abyssal mixing. A recent estimate of wind-driving suggests 1 TW of additional mixing power. All values are very uncertain.A surprising conclusion is that the equator-to-pole heat flux of 2000 TW associated with the meridional overturning circulation would not exist without the comparatively minute mechanical mixing sources. Coupled with the findings that mixing occurs at a few dominant sites, there is a host of questions concerning the maintenance of the present climate state, but also that of paleoclimates and their relation to detailed continental configurations, the history of the Earth–Moon system, and a possible great sensitivity to details of the wind system.     

Surface layer mixing during the SAGE ocean fertilization experiment

Vessel-based observations of the oceanic surface layer during the 14-day 2004 SAGE ocean fertilization experiment were conducted using ADCP, CTD and temperature microstructure in a frame of reference moving with a patch of injected SF₆ tracer. During the experiment the mixed layer depth z_mld ranged between 50 and 80 m, with several re-stratifying events that brought z_mld up to less than 40 m. These re-stratifying events were not directly attributable to local surface-down development of stratification and were more likely associated with horizontal variation in density structure. Comparison between the CTD and a one-dimensional model confirmed that the SAGE experiment was governed by 3-d processes. A new method for estimating z_mld was developed that incorporates a component that is proportional to density gradient. This highlighted the need for well-conditioned near-surface data which are not always available from vessel-based survey CTD profiles. A centred-displacement scale, L_c, equivalent to the Thorpe lengthscale, reached a maximum of 20 m, with the eddy-centroid located at around 40 m depth. Temperature gradient microstructure-derived estimates of the vertical turbulent eddy diffusivity of scalar (temperature) material yielded bin-averaged values around 10⁻³ m² s⁻¹ in the pycnocline rising to over 10⁻² m² s⁻¹ higher in the surface layer. This suggests transport rates of nitrate and silicate at the base of the surface layer generate mixed layer increases of the order of 38 and 13 mmol/m²/day, respectively, during SAGE. However, the variability in measured vertical transport processes highlights the importance of transient events like wind mixing and horizontal intrusions.     

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.     

Sensitivity studies with the three-dimensional multi-level model for tidal motion

A three-dimensional multi-level hydrodynamic model has recently been developed and applied to tidal motion in Singapore’s coastal waters. This paper describes a series of numerical experiments to evaluate the sensitivity of the tidal currents and elevations to model parameters. The results show that the predicted tidal elevations are insensitive to three model parameters: horizontal eddy viscosity coefficient (Smagorinsky constant, c_h), bottom friction coefficient (c_b) and internal friction coefficient (c_v), whereas the effects of these parameters are quite different for tidal current velocities. The velocities are slightly reduced with an increase in c_h and c_b. The bottom friction effects on velocity profiles increase with water depth. The effect of c_v might be significant for the tidal velocities at all levels. The velocities at upper layers of the water column decrease with the increase in c_v, whereas the velocities at the bottom layer show the reverse trend. The effects of three model parameters on the magnitude and phase of the simulated currents are in the order (from strong to weak) of c_v, c_b and c_h.     

The AMANDES tidal model for the Amazon estuary and shelf

The AMANDES project aims to study transports from the Andean mountains to the Atlantic Ocean through the Amazon system. This requires realistic estuarine modelling in this area strongly forced by tides and river discharge. As none of the existing models for this region would fit the actual needs of the project, a specific new generation model has been implemented.The model is based on the hydrodynamic finite element model T-UGOm. In a first step, we limit our investigations to tidal dynamics. As the Amazon estuary is a very shallow macro-tidal area, it is necessary to improve the available bathymetries and to develop a precise bottom friction parametrisation.In this paper, we discuss the implementation of a high resolution regional model. This allows us to develop a precise and accurate tidal model: for instance, the overall root mean square error on complex differences is reduced from 54 cm in a standard model to 27 cm in our best model. Such precise and accurate tidal modelling is a prerequisite for modelling particle transport.