Effect of spatial inhomogeneity of the resistance coefficient on the dynamics of the <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript> tidal wave in the White Sea

To find variations in the dynamics of the surface M ₂ tide in the White Sea induced by the spatially inhomogeneity of the resistance coefficient, we use a modified version of the QUODDY-4 three-dimensional finite-element hydrostatic model. This version differs from the original version in that it has a module introduced to calculate the resistance coefficient in the bottom boundary layer (BBL). The resistance coefficient is found from resistance laws for an oscillating rotating turbulent BBL over hydrodynamically rough and partially rough (smoothly rough) underlying surfaces describing the dependence of the resistance coefficient and other integral characteristics of resistance on dimensionless similarity parameters: the sea-bottom Rossby number Ro, the streaming Reynolds number Re, and the relative (normalized to tidal frequency) inertial frequency f/σ. The use of spatial inhomogeneity of the resistance coefficient was shown not to lead to considerable changes in tidal characteristics. The values of these characteristics are several times larger than the instrumental measurement errors for the level and velocity but less than the errors in their calculation.     

Weak dependence of the SWAN wave model on hydrodynamic properties of sea bottom

The third generation of the SWAN wave model is modified by the incorporation of new resistance laws for hydrodynamically rough, incompletely rough (smoothly rough), and smooth underlying surfaces. A modified model is used to determine the functional dependences of wave parameters (such as the dimensionless energy of waves and the dimensionless spectral peak frequency) on a dimensionless fetch. The results of calculations are compared to the experimental data obtained in Lake George (northeastern Australia), which has a nearly constant depth and extended, nearly rectilinear segments of coast. The SWAN model is shown to depend weakly on hydrodynamic properties of the sea bottom: distinctions arising from changes in hydrodynamic properties of the sea bottom are smaller than the variances of experimental estimates.     

Rational approach to the bottom shear stress in tidal planetary boundary layer flow

The friction velocity associated with the maximum bottom shear stress in neutrally stable tidal planetary boundary layer flow is presented. The directions of the bottom shear stresses for the anticlockwise and clockwise rotating components are also presented. The results are obtained by using similarity theory and are given for flow conditions in the rough, smooth and transitional smooth-to-rough turbulent regime. An approximation for the maximum bottom shear stress by disregarding the rotation of the velocity in the boundary layer as the seabed is approached is also presented.     

珠江河口底边界层憩流动力特征

通过在珠江黄茅海河口进行的25 h定点连续观测,分析了潮流底边界层在憩流时刻的动力特征。结果表明,憩流期非恒定性增强,改变了平均流和湍流结构。主要表现:1)平均流结构出现三种不同类型,分别是对数分布(摩擦力主导)、垂向均匀分布(惯性主导)和过渡状态(摩擦力和惯性力平衡);2)湍流各向异性增强,湍谱惯性子区带宽减小。各湍流特征参数在转流时刻达到最小值,表明惯性作用抑制了湍流的发育。     

一种三次多项式湍黏性底边界层的流场分布

本文通过假定底边界层湍黏性的三次多项式参数化形式,基于简化的Navier–Stokes方程,并利用超几何方程的性质,推导出了湍流粗糙底边界层的速度解析解。同时,得到了底边界层内其他的动力参数,如底剪应力、Ekman传输、Ekman抽吸及近底部速度分布场,从理论上讨论了均匀混合底边界层特征量分布特征。通过数值结果分析,进一步得出底边界层的总速度、亏损速度及其剪应力受平均流的角频率和地球自转影响比较大;而底边界层的动力结构对于底边界层顶部粗糙度不敏感。该涡黏性模式从理论上丰富了底边界层涡黏性的形式,为底边界层的动力系统研究提供了借鉴和理论参考。     

Field Observation and Analysis of Wave-Current-Sediment Movement in Caofeidian Sea Area in the Bohai Bay, China

In order to study the mechanism of flow-sediment movement, it is essential to obtain measured data of water hydrodynamic and sediment concentration process with high spatial and temporal resolution in the bottom boundary layer (BBL). Field observations were carried out in the northwest Caofeidian sea area in the Bohai Bay. Near 2 m isobath (under the lowest tidal level), a tripod system was installed with AWAC (Acoustic Wave And Current), ADCP (Acoustic Doppler Current Profilers), OBS-3A (Optical Backscatter Point Sensor), ADV (Acoustic Doppler Velocimeters), etc. The accurate measurement of the bottom boundary layer during a single tidal period was carried out, together with a long-term sediment concentration measurement under different hydrological conditions. All the measured data were used to analyze the characteristics of wave-current-sediment movement and the BBL. Analysis was performed on flow structure, shear stress, roughness, eddy viscosity and other parameters of the BBL. Two major findings were made. Firstly, from the measured data, the three-layer distribution model of the velocity profiles and eddy viscosities in the wave-current BBL are proposed in the observed sea area; secondly, the sediment movement is related closely to wind-waves in the muddy coast area where sediment is clayey silt: 1) The observed suspended sediment concentration under light wind conditions is very low, with the peak value generally smaller than 0.1 kg/m3 and the average value being 0.03 kg/m3; 2) The sediment concentration increases continuously under the gales over 6-7 in Beaufort scale, under a sustained wind action. The measured peak sediment concentration at 0.4 m above the seabed is 0.15-0.32 kg/m3, and the average sediment concentration during wind-wave action is 0.08-0.18 kg/m3, which is about 3-6 times the value under light wind conditions. The critical wave height signaling remarkable changes of sediment concentration is 0.5 m. The results show that the suspended load sediment concentration is mainly influenced by wave-induced sediment suspension.     

Bottom Boundary Layer Characteristics in the Hooghly Estuary Under Combined Wave-Current Action

The development of a theoretical model for estimating bottom boundary layer characteristics in the Hooghly estuary, located in the east coast of India, under combined effects of waves and currents is reported. Three numerical models, viz a depth averaged hydrodynamic model, SWAN wave model, and bottom boundary layer model, were integrated. In the bottom boundary layer parameters, maximum bottom stress, effective friction factor, and near-bed velocity both during ebb and flood phases of the tidal forcing are investigated and validated for the Haldia channel. The close match seen from results signifies applicability of this model for entire Hooghly basin.     

Field observation and analysis of wave-current-sediment movement in Caofeidian Sea area in the Bohai Bay,China

In order to study the mechanism of flow-sediment movement, it is essential to obtain measured data of water hydrodynamic and sediment concentration process with high spatial and temporal resolution in the bottom boundary layer （BBL）. Field observations were carried out in the northwest Caofeidian sea area in the Bohai Bay. Near 2 m isobath （under the lowest tidal level）, a tripod system was installed with AWAC （Acoustic Wave And Current）, ADCP （Acoustic Doppler Current Profilers）, OBS-3A （Optical Backscatter Point Sensor）, ADV （Acoustic Doppler Velocimeters）, etc. The accurate measurement of the bottom boundary layer during a single tidal period was carried out, together with a long-term sediment concentration measurement under different hydrological conditions. All the measured data were used to analyze the characteristics of wave-current-sediment movement and the BBL. Analysis was performed on flow structure, shear stress, roughness, eddy viscosity and other parameters of the BBL. Two major findings were made. Firstly, from the measured data, the three-layer distribution model of the velocity profiles and eddy viscosities in the wave-current BBL are proposed in the observed sea area; secondly, the sediment movement is related closely to wind-waves in the muddy coast area where sediment is clayey silt： 1） The observed suspended sediment concentration under light wind conditions is very low, with the peak value generally smaller than 0.1 kg/m^3 and the average value being 0.03 kg/m^3; 2） The sediment concentration increases continuously under the gales over 6-7 in Beaufort scale, under a sustained wind action. The measured peak sediment concentration at 0.4 m above the seabed is 0.15-0.32 kg/m^3, and the average sediment concentration during wind-wave action is 0.08-0.18 kg/m^3, which is about 3-6 times the value under light wind conditions. The critical wave height signaling remarkable changes of sediment concentration is 0.5 m. The results show that the suspended load sediment concentration is mainly influenced by wave-induced sediment suspension.     

半封闭海区潮波运动问题的构建

利用海底粘滞性条件,首先导出了海底摩擦与海面坡度之间的简单关系式,在此基础上导出了水平流通量与海面坡度的关系式。然后利用连续性方程进一步得到了海面升高即潮位所满足的二阶椭圆型方程,进而导出了以潮位形式给出的半封闭海区岸壁不可穿透条件。最终在给定半封闭海区开边界水位分布的条件下构建了完整的关于潮位分布函数的微分方程边值问题。初步讨论表明,海底摩擦矢量与水平流通量矢量并不在相反的方向上。     

On a theoretical model of rough turbulent wave boundary layers

An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.     

Pathways of suspended particles transport in the bottom layer of the southern Baltic Sea depending on the wind forcing (Numerical Simulation)

A random-walk model for a nonuniform diffusivity media coupled with an ocean circulation model has been applied to describe the pathways of suspended particles transport in the bottom boundary layer (BBL) of the southern Baltic Sea. The circulation model is based on the Princeton Ocean Model, in which the vertical grid size is logarithmically refined towards the bottom in order to resolve the BBL. Fields of the flow velocity and eddy diffusivities simulated by the POM, along with the settling velocity of the suspended particles, are used as an input for the random-walk model. A number of numerical experiments were performed to study the pathways of suspended particles in the southern Baltic BBL depending on the wind conditions. In particular, the suspended particles introduced into the BBL in the center of the Bornholm Basin at westerly and southerly winds are found to be trapped in the basin provided that the particles’ settling velocity is equal or greater than 2 m/day. The trapping phenomenon is explained by the combined effect of the Ekman transport convergence in the BBL due to the cyclonic gyre and the gravitational settling of the particles.     

Modelling of the barotropic processes in the Bohai Sea

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珠江磨刀门河口潮波振幅梯度与上下游动力边界的关系异变研究

强人类活动目前已经成为河口演变的主要动力。阐明流量驱动下河控型河口潮波传播演变过程及机制,对河口治理及人类活动的影响评价具有重要指导意义。以珠江磨刀门河口为例,研究了径潮动力阶段性演变特征。采用流量驱动的R_TIDE数据驱动模型探究了该区潮波振幅梯度和上下游动力边界(即上游流量和口门振幅)关系的变化规律。结果表明,在强人类活动影响下,各潮位站M₂分潮振幅明显上升(三灶站除外),且具有季节性差异和阶段性变化,灯笼山-马口河段的M₂分潮振幅沿程平均增大约0.07 m,河段潮波振幅梯度平均增大约4.61×10^–6 m^–1。研究潮波振幅梯度与上下游动力边界的阈值的关系表明,阈值效应主要出现在甘竹-马口河段。在强人类活动影响下,潮波振幅梯度阈值增大,相应的流量阈值增大,而振幅阈值基本不变。在达到振幅阈值之前,由于底床摩擦效应,大潮振幅衰减效应大于小潮,而在超过振幅阈值后,地形辐聚效应成为影响潮波振幅梯度变化的主要因素,大潮振幅衰减效应小于小潮。阈值的变化主要与流量、地形、摩擦等多因子耦合作用有关,当地形辐聚效应和底床摩擦效应达到平衡时,潮波振幅梯度与上下游动力边界之间则出现阈值效应。该现象的发现可为河口海岸防灾减灾和水资源管理等实际问题提供重要理论支撑。     

Significance of Shallow Bottom Friction in the Dynamics of the Tsushima Current

A simple analytical model is considered for the dynamics of volume transport of the Tsushima Current. This model is basically baroclinic but allows bottom friction over the shallow regions connecting the Pacific Ocean to the Japan Sea basin, and is thus different from previous models which are either purely barotropic with bottom friction predominating over the whole domain, or purely baroclinic with bottom friction completely ignored. Compared to the previous barotropic model, this model is not only more realistic but also gives much simpler results. It gives the observed downstream sea level slope, which is not seen in the previous baroclinic model. As a result, the estimated transport of the Tsushima Current is closer to the observational data than those of previous models. This model indicates that the localized bottom friction acting over the shallow regions not only controls the transport of the Tsushima Current but also moves the stagnation point of the western boundary current northward. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

A numerical study on the tidal residual flow

Characteristics of the tidal residual flow, the steady current induced in the tidal current system, are studied by a numerical method. The model basin has the same topography as that studied byYanagi (1976) and byOonishi (1977) where only the horizontal motion of the residual flow is concerned. In this study, the effect of the vertical motion is investigated as it is associated with the tidal residual flow. To this end, the bottom friction omitted in the previous study (Oonishi, 1977) is included and a two-leveled model is adopted.The first two experiments exclude the earth's rotation and the buoyancy effect on the flow. The results are as follows. The horizontal flow pattern is essentially the same as that obtained in the previous Oonishi study. The bottom friction results in the reduction of the velocity of the residual flow especially in the bottom level. An important result is that vertical velocity is as strong as the horizontal velocity multiplied by the scale ratio and that it remains even in the time-average. Upwelling appears at the center of the residual circulation. This upwelling explains Yanagi's observation in the hydraulic model that the sediment is swept by the flow and accumulates horizontally in the area at the bottom below the center of the residual circulation. The distribution of a tracer, which is simultaneously calculated in these cases, indicates the important role of vertical motion in the material dispersion in the model.The last experiment includes the earth's rotation and the buoyancy effect presuming a more actual sea. It shows another effect of the vertical motion. The Coriolis term, which operates only under the condition that a horizontal divergence of the flow is present, skews the horizontal residual flow pattern.     

Tidal boundary layer measurements in the presence of waves

Measurements of tidal current and wave velocity made at 0.69 and 1.85 m above a rough seafloor exhibit large current gradients (boundary layer) in the water column. The logarithmic boundary layer flow model was fitted to the measurements, and thus roughness (z₀) and friction velocity (u^*) parameters were derived. The roughness parameter values were generally consistent with the observed upstream physical roughness. The values of both parameters for conditions in the rough turbulence flow regime are generally larger (much larger for ebb) than earlier published values for similar measurements of currents in the absence of significant waves but are comparable to values from recent measurements of currents in the presence of storm waves. The high parameter values here appear to relate more to the magnitude of the current and to the upstream physical bottom roughness than to the magnitude of the seastate. Large boundary layers in the flow at the seabed have a profound effect on the design of offshore structures such as offshore pipelines.     

Transport and bottom boundary layerobservations of the North Atlantic Deep Western Boundary Current at the Blake Outer Ridge

The North Atlantic Deep Western Boundary Current (DWBC) was surveyed at the Blake Outer Ridge over 14 days in July and August 1992 to determine its volume transport and to investigate its bottom boundary layer (BBL). This site was chosen because previous investigations showed the DWBC to be strong and bottom-intensified on the ridge’s flanks and to have a thick BBL. The primary instrument used was the Absolute Velocity Profiler, a free-falling velocity and conductivity–temperature–depth device. In two sections across the width of the DWBC, volume transports of 17±1 Sv and 18±1 Sv were measured for all water flowing equatorward below a potential temperature of 6°C (1 Sv=1×10⁶ m³ s^-1). Transport values were derived using both absolute velocities and AVP-referenced geostrophic velocities and were the same within experimental uncertainty. Good agreement was found between our results and historical ones when both were similarly bounded and referenced. Although this was a short-term survey, the mean of a 9-day time series of absolute velocity profiles was the same as the means of year-long current-meter records at three depths in the same location. A turbulent planetary BBL was found everywhere under the current. The thickness of the bottom mixed layer (BML), where concentrations of density, nutrients, and suspended sediments were vertically uniform, was asymmetrical across the current and up to 5 times thicker than the BBL. There was no velocity shear above the BBL within the thicker BMLs, and the across-slope density gradient was very small. The extra-thick BML is perhaps maintained by a combination of processes, including turbulence, downwelling Ekman transport, a weak up-slope return flow above the BBL, and buoyant convection from the BBL into the BML. The frictional bottom stress was mostly balanced by a down-stream change in the current’s external potential energy evidenced by a drop in the velocity core of the current.     

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。     

Bottom boundary layer in the Black Sea: Experimental data,turbulent diffusion,and fluxes

Measurements of 14 vertical profiles of currents and hydrological parameters in the near-bottom layer with a depth resolution of 0.1 m were carried out in several regions of the Black Sea shelf, at five points over the continental slope, and in three deep water regions. The upper boundary of the benthic boundary layer (BBL) was reliably determined at a point at a distance from 5–7 to 35–40 m from the bottom where the gradients of the density and the velocity of the currents changed. The experimental data obtained were used to determine the coefficient of the bottom friction, the friction velocity, the coefficients of the vertical diffusion of momentum and density, and the vertical fluxes of temperature and salinity in the BBL.