Tide simulation using the mild-slope equation with Coriolis force and bottom friction

Since the mild-slope equation was derived by Berkhoff (1972),the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,some scholars applied the mild-slope equation in simulating the tidal motion,which proves that the equation is capable to calculate the tide in actual terrain.But in their studies,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.     

北部湾潮波数值研究

利用普林斯顿海洋模式(POM08)建立了北部湾及其临近海区潮汐潮流数值模式,模拟了K1,O1,M2和S2这4个主要分潮,分析了模拟的潮汐和潮流分布特征,从潮波能量的角度讨论了琼州海峡对北部湾潮波系统的影响,并给出北部湾潮能的耗散情况。研究表明,北部湾是典型的全日潮海区,K1和O1分潮在南部湾口形成半个旋转潮波系统,无潮点位于越南顺安附近岸边。琼州海峡中的欧拉潮汐余流为西向流,潮余流造成的水通量约为0.034×106m3/s;余流出海峡西口后,先折向北,然后转向南流出湾外。研究海区中两个强潮流区分别位于琼州海峡和海南岛的西侧,同时这也是两个潮能的高耗散区。北部湾的潮能自南部湾口由外海传入,通过西口涌入琼州海峡,到达海峡东口时日潮波的能量已基本耗散殆尽,在海峡内耗散的4个分潮的潮能约为3.33 GW,相当于北部湾潮能耗散量的35%左右。数值试验表明,琼州海峡作为潮能耗散的重要海区,其存在对于北部湾潮波系统的形成具有较大影响。计算了底边界潮能耗散,结果表明在北部湾和琼州海峡,底边界耗散的潮能分别占该海区总耗散的83%和80%。     

长江口潮波传播影响因素探讨

在河口潮波计算假定的基础上,概化长江口崇明岛南侧水域,建立了三种概化模型,探讨影响长江口潮波传播的因素.计算表明,潮波传播是地形、河口平面形状和底摩阻共同作用的结果,河口平面收缩对潮波传播影响最大,其次为河床底摩擦作用,然后是河口断面面积变化.     

内潮耗散与自吸-负荷潮对南海潮波影响的数值研究

利用非结构三角形网格的FVCOM海洋数值模式,在其传统二维潮波方程中加入参数化的内潮耗散项和自吸-负荷潮项,计算了南海及其周边海域的M_2、S_2、K_1和O_1分潮的分布。与实测值的比较表明,引入这两项对模拟准确度的提高有明显效果。根据模式结果本文计算分析了研究海域的潮能输入和耗散。能量输入计算表明,能通量是潮能输入的最主要构成部分,通过吕宋海峡断面进入南海的M_2和K_1分潮能通量分别为38和29GW;半日周期的自吸-负荷潮能量输入以负值居多,而全日周期的自吸-负荷潮能量输入以正值居多,因而自吸-负荷潮减弱了南海的半日潮,并加强了南海的全日潮。引潮力的作用也减弱了半日潮而加强了全日潮,但其作用要小于自吸-负荷潮。潮能耗散的分析显示底摩擦耗散在沿岸浅水区域起主导作用,内潮耗散则主要发生在深水区域。内潮耗散的最大值出现在吕宋海峡,且位于南海之外的海峡东部的耗散量大于位于南海之内的海峡西部的耗散量。对M_2和K_1分潮吕宋海峡的内潮耗散总值分别达到16和23GW。     

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。     

考虑发电机尾流作用的潮流能理论可开发量的评估

In this study, we construct one 2–dimensional tidal simulation, using an unstructured Finite Volume Coastal Ocean Model(FVCOM). In the 2–D model, we simulated the tidal turbines through adding additional bottom drag in the element where the tidal turbines reside. The additional bottom drag was calculated from the relationship of the bottom friction dissipation and the rated rotor efficiency of the tidal energy turbine. This study analyzed the effect of the tidal energy turbine to the hydrodynamic environment, and calculated the amount of the extractable tidal energy resource at the Guishan Hangmen Channel, considering the rotor wake effect.     

磨刀门河口枯季波生流场数值模拟研究

本文建立曲线坐标系下的双曲型缓坡方程波浪模型和考虑波浪辐射应力影响的深度平均2D潮流数学模型,首次研究了磨刀门河口2011年地形条件下的枯季波生流场。受波浪作用影响,落潮阶段,波浪作用方向与流向相反,在波浪顶托效应下拦门沙沙脊及外坡处流速普遍减小,形成两个主要回流区,口门外东西两侧浅滩处流速也减小,东西两汊及横洲深槽流速增大;涨潮阶段,波浪作用方向与流向相同,拦门沙沙脊及外坡处流速增大,沙脊处出现冲越流,口门两侧浅滩处流速增大,横洲深槽流速减小。     

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%)。     

崇明岛南侧盐沼潮滩消能状态研究

沿海盐沼潮滩可以有效降低波浪高度,耗散波浪能量,在海岸防护和沿海城市安全中扮演着重要角色。以长江河口崇明岛南侧盐沼潮滩为对象,基于不同潮间带实测波浪变化数据,采用波能衰减模型对波浪横向沿潮滩衰减状态进行定量分析,由此探讨波浪衰减主控要素。结果表明:波浪沿盐沼潮滩向岸传播过程中,波高以及波能大幅下降,其中光滩—芦苇前部区域波能平均下降19%,芦苇区域波能平均下降71%,有植被覆盖区域对波浪的衰减效应更为显著。同时,水深、入射波高及阻力是影响盐沼潮滩波浪衰减的主要因素,波浪衰减强度随水深增大而减小,入射波高增加以及阻力的增大而增强。     

灌河口潮汐不对称数值模拟研究

建立灌河口平面二维潮流数字模型,并在灌河口口门至陈家港河段沿程布置5个采样点和3个横向断面,通过对各采样点一个月数值模拟结果进行调和分析,得出灌河口M2分潮及其主要倍潮的基本特征,然后利用潮位-流速关系图及通过对动量方程中各项的统计计算,研究了灌河口潮波运动的基本动力平衡、M2的主要倍潮的产生机制及其对潮汐不对称现象的影响。研究认为:灌河口潮汐潮流均属正规半日潮型。M4、M6分潮对于灌河口潮波变形有着重要的影响,M8分潮除在浅滩处外对潮汐不对称的影响很小。在深槽处M4分潮导致最大落(涨)潮流速减小(增大),最大涨(落)潮流速与最高(低)潮位之间的相位差增大。M6分潮的影响与M4基本一致,但其作用明显小于M4分潮。在浅滩处M4分潮导致最大涨落潮流速均大于M2分潮的值,M6和M8分潮使最大涨落潮流速均出现在高潮位附近,但M6、M8使最大涨潮流速减小,而使最大落潮流速增大。外海边界处倍潮波的传入对于口门附近的潮汐不对称有一定影响。M4和M6分潮导致灌河口的潮汐不对称表现为涨潮主导型,潮波运动主要受到压强梯度力、非线性对流和底摩擦力,三者与局地惯性力构成灌河口的基本动力平衡,摩擦力并不是最重要的作用力。     

The decomposition and simulation of the longitudinal circulation in a coastal lagoon

Current measurements during a 32-day study period in late spring, 1977, are used to quantify the magnitude and relative importance of tidal and wind-driven motion in the interior of the Indian River lagoon, on the Atlantic coast of Florida. Harmonic analysis of the total longitudinal flow along the axis of the lagoon isolates the tidal component of the current; non-tidal flow is revealed by subtracting the tidal current from the total current, and making corrections for non-linear relationships between the current and both surface wind stress and bottom friction. A one-layer, one-dimensional model is developed to simulate wind drift. A quadratic bottom friction term with a drag coefficient of 15 × 10^?3 gives results which compare most favourably with observations. Results indicate that tidal forcing explains approximately 45% of the total variance at the study site, 25 km from the nearest inlet. Local wind forcing accounts for 44% of the non-tidal flow. The remainder of the variance is attributed to freshwater outflow through the lagoon and non-local forcing.     

Depth- and current-induced effects on wave propagation into the Altamaha River Estuary, Georgia

A study of sea surface wave propagation and its energy deformation was carried out using field observations and numerical experiments over a region spanning the midshelf of the South Atlantic Bight (SAB) to the Altamaha River Estuary, GA. Wave heights on the shelf region correlate with the wind observations and directional observations show that most of the wave energy is incident from the easterly direction. Comparing midshelf and inner shelf wave heights during a time when there was no wind and hence no wave development led to an estimation of wave energy dissipation due to bottom friction with corresponding wave dissipation factor of 0.07 for the gently sloping continental shelf of the SAB. After interacting with the shoaling region of the Altamaha River, the wave energy within the estuary becomes periodic in time showing wave energy during flood to high water phase of the tide and very little wave energy during ebb to low water. This periodic modulation inside the estuary is a direct result of enhanced depth and current-induced wave breaking that occurs at the ebb shoaling region surrounding the Altamaha River mouth at longitude 81.23°W. Modelling results with STWAVE showed that depth-induced wave breaking is more important during the low water phase of the tide than current-induced wave breaking during the ebb phase of the tide. During the flood to high water phase of the tide, wave energy propagates into the estuary. Measurements of the significant wave height within the estuary showed a maximum wave height difference of 0.4 m between the slack high water (SHW) and slack low water (SLW). In this shallow environment these wave–current interactions lead to an apparent bottom roughness that is increased from typical hydraulic roughness values, leading to an enhanced bottom friction coefficient.     

A note on wave action conservation in a dissipative current wave motion

We consider steady, slowly varying water waves propagating on a steady current over a gently sloping bed, so-called current depth refraction. All expressions are correct to second order in wave amplitude. Formulating the energy equation for the fluctuating motion in terms of wave action (wave energy divided by intrinsic angular frequency) results in an expression, where the dissipative term is strikingly similar to wave action itself. It is simply the ‘extra’ dissipation (per unit area) caused by the fluctuating motion (i.e. total dissipation minus the effect of current acting on total mean bed shear stress) divided by the intrinsic angular frequency. We call it ‘wave action dissipation’. An inconsistency in Phillips' (1977) book is pointed out. A new formula for the calculation of wave amplitudes along rays is set forth.     

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.     

Modified mild slope equation and open boundary conditions

A numerical model to compute wave field is developed. It is based on the Berkhoff diffraction-refraction equation, in which an energy dissipation term is added, to take into account the breaking and the bottom friction phenomena. The energy dissipation function, by breaking and by bottom friction, is introduced in the Berkhoff equation to obtain a new equation of propagation.The resolution is done with the hybrid finite element method, where lagrangians elements are used.     

Reynolds stress and TKE production in an estuary with a tidal bore

We report new measurements of the turbulent properties of the flow in a tidally energetic estuarine channel of almost uniform cross-section. A high-frequency (1.2 MHz), bottom-mounted Acoustic Doppler Current Profiler (ADCP) has been used to observe the velocity field at a sampling rate of 10 Hz in parallel with measurements of the surface elevation by tide gauges. Our data have been analysed using the Variance Method to determine turbulent kinetic energy (TKE), shear stress and TKE production over the tidal cycle with a time resolution of 60 s. During the highly energetic but brief flood period, when the surface axial velocity reaches 2 m s⁻¹, we observed large values of stress (>2 Pa) and shear production (5 W m⁻³). TKE is also input through the release of energy in the bore itself which results in a brief but intense injection of energy at the bore front with large transient TKE levels (100 J m⁻³). Subsequent input by shear production maintains TKE levels which are generally lower (20 J m⁻³) than the strong peak associated with the bore for the rest of the flood. On the ebb, the flow is relatively tranquil with maximum speeds 0.5 m s⁻¹ and peak TKE production rates of 0.1 W m⁻³.The flow and elevation data have also been used to estimate the energy fluxes into and out of the estuary. Short (1 h), intense energy inputs (8 MW at springs) on the flood flow are largely balanced by longer, less intense seaward energy flow on the ebb. The net energy input is found to be 0.1 MW at springs which is consistent with estimates of upstream dissipation. Peak dissipation in the bore itself may exceed the mean energy input but it is active only for a small fraction of the tidal cycle and its average contribution does not exceed 12% of total dissipation.     

象山港潮波响应和变形研究──Ⅰ.观测和分析

利用实测资料分析了象山港海湾对潮波的响应和湾内潮波变形.结果说明象山港对外海传入的半日潮波的振幅有明显的放大作用.M₄和MS₄两个浅水分潮在湾内快速增长造成了潮波变形和潮不对称性.潮波非线性的沿程变化和不同区域的潮能耗散说明湖滩与潮波变形关系不大,而湖波非线性在牛鼻水道中的增强对湾内潮波变形是重要的,1/4日分潮在湾内的共振作用也对M₄和MS₄两个浅水分潮起了放大作用.     

波流共同作用下珊瑚礁冠层附近平均流分布及阻力特性试验

本文通过物理模型试验研究了波流共同作用下珊瑚礁冠层附近平均流的分布特征以及阻力特性,分析了典型波浪工况下无潮流、正向潮流和反向潮流分别作用下平均流速、摩阻流速、阻力系数的沿礁变化规律。结果表明：无潮流时礁前斜坡及外礁坪上存在海底回流且在礁缘附近回流最强,在礁坪上冠层附近平均流表现为向岸流,且该流沿礁向海岸方向持续增大。相较于无潮流时,正向潮流作用下冠层内外均为向岸流,在礁坪上冠层内外的向岸流显著增大;反向潮流作用下冠层内外均为离岸流且在礁缘处达到最大,该离岸流在礁坪上逐渐减小然后趋于稳定。无潮流时礁坪上摩阻流速呈小幅波动;相较于无潮流时,正向潮流、反向潮流影响下礁坪上摩阻流速显著增大,其中正向潮流影响下增幅更大;无潮流时礁坪上水力粗糙度沿礁减小,正向潮流和反向潮流影响下水力粗糙度普遍有幅度不等的增加。三种工况下礁坪上的阻力系数均沿礁整体呈下降趋势,相较于无潮流时,正向潮流和反向潮流影响下礁坪上的阻力系数显著增大,且正向潮流作用时增幅更大。     

Local balance in the air-sea boundary processes

A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10^?2 andK=2.16×10^?5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean. “The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves. Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.     

Tidal and river discharge forcing upon water and sediment circulation at a rock-bound estuary (Guadiana estuary,Portugal)

The relative impacts of tidal (neap, spring) and river discharge (including a flood event) forcing upon water and sediment circulation have been examined at the rock-bound Guadiana estuary. Near-bed and vertical profiles of current, salinity, turbidity, plus surface suspended sediment concentrations (SSC, at some stations only), were collected at the lower and central/upper estuary during tidal and fortnightly cycles. In addition, vertical salinity and turbidity profiles were collected around high and low water along the estuary. Tidal asymmetry produced faster currents on the ebb than on the flood, especially at the mouth. This pattern of seaward current dominance was enhanced with increasing river flow, due to horizontal advection that was confined within the narrow estuarine channel. The freshwater inputs and, at a degree less, the tidal range controlled the vertical mixing and stratification importance. Well-mixed (spring) and partially stratified (neap) conditions alternated during periods of low river flows, with significant intratidal variations induced by tidal straining (especially at the partially stratified estuary). Highly stratified conditions developed with increasing river discharge. Intratidal variability in the pycnocline depth and thickness resulted from current shear during the ebb. A salt wedge with tidal motion was observed at the lower estuary during the flood event. Depending on the intensity of turbulent mixing, the residual water circulation was dominantly controlled either by tidal asymmetry or gravitational circulation. The SSC was governed by cyclical local processes (resuspension, deposition, mixing, advection) driven by the neap-spring fluctuations in tidal current velocities. More, intratidal variability in stratification indicated the significance of tidal pumping at the partially and highly stratified estuary. The estuary turbidity maximum (ETM) was enhanced with increasing current velocities, and displaced downstream during periods of high river discharge. During the flood event, the ETM was expelled out of the estuary, and the SSC along the estuary was controlled by the sediment load from the drainage basin. Under these highly variable river flow conditions, our observations suggest that sand is exported to the nearshore over the long-term (>years).