A Comprehensive Lagrangian Transport Study in A Long-Narrow Bay,Xiangshan Bay,China

Study on the transport and mixing in coastal waters is of great concern to the ocean resources exploitation and ecological system protection. Lagrangian methods are direct and effective of researching mass transport. Two Lagrangian tools were adopted and combined to describe water transport in a long-narrow bay, Xiangshan Bay,China. Based on the fields of tidal velocity simulated from the 3-D hydrodynamic model, Lagrangian Coherent Structures(LCSs) and synoptic Lagrangian maps(SLMs) were calculated in the study area. Through comparison of the results, the features and relation of the two tools were discussed. The results show that the LCSs act as the separatrix of the water regions with different transport characteristics and can identify the water areas with different transport time scales. The comprehensive application of the Lagrangian tools is helpful to obtain more insight into the water transport process.     

Estuary/ocean exchange and tidal mixing in a Gulf of Maine Estuary: A Lagrangian modeling study

A Lagrangian particle method embedded within a 2-D finite element code, is used to study the transport and ocean–estuary exchange processes in the well-mixed Great Bay Estuarine System in New Hampshire, USA. The 2-D finite element model, driven by residual, semi-diurnal and diurnal tidal constituents, includes the effects of wetting and drying of estuarine mud flats through the use of a porous medium transport module. The particle method includes tidal advection, plus a random walk model in the horizontal that simulates sub-grid scale turbulent transport processes. Our approach involves instantaneous, massive [O(500,000)] particle releases that enable the quantification of ocean–estuary and inter-bay exchanges in a Markovian framework. The effects of the release time, spring–neap cycle, riverine discharge and diffusion strength on the intra-estuary and estuary–ocean exchange are also investigated.The results show a rather dynamic interaction between the ocean and the estuary with a fraction of the exiting particles being caught up in the Gulf of Maine Coastal Current and swept away. Three somewhat different estimates of estuarine residence time are calculated to provide complementary views of estuary flushing. Maps of residence time versus release location uncover a strong spatial dependency of residence time within the estuary that has very important ramifications for local water quality. Simulations with and without the turbulent random walk show that the combined effect of advective shear and turbulent diffusion is very effective at spreading particles throughout the estuary relatively quickly, even at low (1 m²/s) diffusivity. The results presented here show that a first-order Markov Chain approach has applicability and a high potential for improving our understanding of the mixing processes in estuaries.     

Interactions of nonlinear gravity waves and uniform current in Lagrangian system

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an EulerLagrange transformation. The thirdorder asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformlyvalid. The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.     

Numerical Simulation of Water Exchange Characteristics of the Jiaozhou Bay Based on A Three-Dimensional Lagrangian Model

Based on theory of three-dimensional hydrodynamics,an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay.The three-dimensional hydrodynamic model,driven by tide and wind,is used to study the effects of wetting and drying of eatuarine intertidal flats by the dry-wet grid technology based on the Estuarine,Coastal and Ocean Model (ECOM).The particle model includes the advection and the diffusion processes,of which the advection process is simulated with a certain method,and the diffusion process is simulated with the random walk method.The effect of the intertidal zone,the turbulent diffusion and the timescales of the water exchange are also discussed.The results show that a moving boundary model can simulate the transport process of the particle in the intertidal zone,where the particles are transported for a longer distance than that of the stationary result.Simulations with and without the turbulent random walk show that the effect of turbulent diffusion is very effective at spreading particles throughout the estuary and speeding up the particle movement.The spatial distribution of residence time is given to quantify the water exchange capability that has very important ramifications to water quality.The effect of wind on the water exchange is also examined and the southeasterly wind in summer tends to block the water exchange near the northeast coast,while the northerly wind in winter speeds up the transport process.These results indicate that the Lagrangian particle model is applicable and has a large potential to help understanding the water exchange capability in estuaries,which can also he useful to simulate the transport process of contaminant.     

深海钢悬链立管触地点动力响应分析

研究深海钢悬链立管(SCR)在海洋环境载荷作用下的动力响应.利用非线性弹簧模拟立管与海床触地点的耦合模型,通过模态分析得到钢悬链立管的动力特性参数;时域动力响应分析获得不同工况下触地点及典型部位的位移、弯矩和应力时程.比较分析表明:浮体垂荡运动对触地点的应力状态影响较大,触地点附近存在钢悬链立管动力响应过程中的位移极值点和弯矩极值点.所提方法为触地点区域模拟分析提供了新思路,给出的分析结论对钢悬链立管设计有一定借鉴意义.     

Numerical study on tidal currents and seawater exchange in the Benoa Bay, Bali, Indonesia

A three-dimensional （3-D） finite volume coastal ocean model （FVCOM） was used for the study of water cir culation and seawater exchange in the Benoa Bay, Bali Island. The M2 tidal component was forced in open boundary and discharge from six rivers was included in the numerical calculation. The M2 tidal elevation produced by the FVCOM has a good agreement with the observation data. The M2 tidal current is also suc cessfully calculated under the ebb tide and flood tide conditions. The non-linear M2 tidal residual current was produced by the coastline geometry, especially surrounding the narrow strait between the Serangan Is- land and the Benoa Peninsula. The tidal residual current also generated two small eddies within the bay and one small eddy in the bay mouth. The salinity distribution influenced by river discharge could be success- fully calculated, where the numerical calculation and the observation results have a good correlation （r2） of 0.75. Finally in order to examine the seawater exchange in the Benoa Bay, the Lagrangian particle tracking method and calculation of residence time are applied. The mechanism of particle transport to the flushing of seawater is depicted clearly by both methods.     

拉格朗日拟序结构分析渤海湾岸线变化对物质输运的影响

科学评估围填海对海洋中物质输运的影响,对海洋环境保护和管理具有重要的意义。本文采用非结构网格有限体积海洋模型 （FVCOM） 模拟渤海湾 2004 年和 2018 年岸线变化前后水动力场,通过拉格朗日拟序结构的方法,评估岸线变化 对物质输运的影响。结果表明：岸线变化后,物质自近岸向湾内的扩散加强,且物质的输运通道和聚集区发生改变。曹妃甸附近原有清晰输运和聚集区域消失,物质向湾内输运;黄骅港阻碍了西部水体沿岸的南下路径,并在防沙堤顶部形成新的聚集区;渤海湾东南区域的物质输运通道向东延伸,输运能力加强,且聚集面积减小。     

Determining the age of water and long-term transport timescale of the Chesapeake Bay

The concept of age of water (AW) is applied to the Chesapeake Bay to investigate the long-term transport properties for dissolved substances. A real-time calibrated hydrodynamic Chesapeake Bay model in 3 Dimensions (CH3D), employing a boundary-fitted curvilinear grid, is used for the study. The long-term transport properties, represented by AW, are investigated under the conditions of low river inflow of 1995 and high river inflow of 1996, as well as for constant mean inflows. The influences of freshwater, density-induced circulation, and wind-induced transport on age distribution have been investigated. Model results show that river inflows, wind stress, and density-induced circulation play important roles in controlling the long-term transport in the Bay. The model results shows that it requires 120–300 days for a marked change in the characteristics of the pollutant source discharged into the Bay from the Susquehanna River to affect significantly the conditions near the mouth under different hydrodynamic conditions. An increase of river discharge results in increases of downstream residual current and gravitational circulation, and thus reduces AW. The density-induced circulation contributes to the transport substantially. The dissolved substances discharged into the Bay are transported out of the Bay more rapidly when the estuary becomes more stratified. Southeasterly and southwesterly winds have strong impacts on the transport compared to the northeasterly and northwesterly winds. The former increases lateral and vertical mixing significantly. Consequently, the gravitational circulation is reduced and the transport time is increased by 50%. The model results provide useful information for understanding the long-term transport processes in the Bay.     

桑沟湾海域物理自净能力分析

在桑沟湾汁算潮流场基础上,采用ADI法,建立了拉格朗日余流模型和平流——扩散输运模型。对排污口的污水输运轨迹进行了跟踪,并预测了桑沟湾1995年、2000年的水质,绐出了COD浓度分布的发展趋势,指出桑沟湾是一个水交换滞缓、物理自净能力较弱的海区。据此可为桑沟湾沿岸的排污口选址提供依据。     

渤海夏季底层环流的观测与模拟

通过分析用人工水母在渤海夏季进行的首次底层环流的 L agrange观测 ,发现在渤海底层 Lagrange余流只有几 cm/s,在海峡处基本是北进南出的情况 ,在辽东湾有 1个逆时针的环流 ,在渤海湾有 1个顺时针的环流。但是进一步分析发现 ,底层人工水母的运移 (代表了物质输运 )并不完全反映环流的方向 ,在有些站位甚至出现相反的趋势。通过数值模拟知道瞬时的扩散及沉降等过程是产生这种结果的原因 ,而根源在于环流场的不均匀性。     

胶莱人工河道水质点输运轨迹的数值模拟

利用二维水动力数学模型模拟胶莱人工河道潮流运动,并分析了胶州湾湾口设置潜堤前后胶莱人工河道水质点的运动轨迹和水位变化过程。结果表明,开通胶莱人工河道能够使黄海的胶东湾海水向渤海的莱州湾输运,但不设置潜堤时从胶州湾到莱州湾的海水输运平均流速较小;设置潜堤后胶州湾水位高于莱州湾水位的时间变长,从黄海到渤海之间的水体输运能够得到加速。计算结果还表明,潜堤顶部与平均水面距离较小时,黄、渤海之间水体输运较快。     

基于拉格朗日拟序结构的黑潮区域海流运输结构提取和分析

海流的拉格朗日运动对于研究物质输送有着重要意义,拉格朗日拟序结构(LCSs)作为研究海流结构的新型方法,相比于传统欧拉方法更为客观。本文提出了一种新的计算LCSs束的方法,基于25年的平均速度场,利用变分方法计算得到黑潮区域的气候态LCSs,并通过简化合并的方法得到了气候态LCSs束,该LCSs束能够突出地显示出海流特性和运输模式,其代表的平均拉格朗日环流有很强的约束作用,且具有鲁棒性。最终我们获得了气候态下12个月份的流场结构图,揭示了月周期性拉格朗日环流规律。本文还利用虚拟粒子输运、多年浮标轨迹以及气候态温盐异常3种方法进行了验证,与拉格朗日运输模式相吻合,证明了海流拉格朗日拟序结构的准确性和可靠性。     

Modeling bed-load transport of coarse sediments in the Great Bay Estuary, New Hampshire

Current, sea level and bed-load transport are investigated in the Lower Piscataqua River section of the Great Bay Estuary, New Hampshire, USA—a well-mixed and geometrically complex system with low freshwater input, having main channel tidal currents ranging between 0.5 and 2 m s⁻¹. Current and sea level forced by the M₂M₄M₆ tides at the estuarine mouth are simulated by a vertically averaged, non-linear, time-stepping finite element model. The hydrodynamic model uses a fixed boundary computational domain and accounts for flooding–drying of tidal flats by making use of a groundwater component. Inertia terms are neglected in comparison with pressure gradient and bottom friction terms, which is consistent with the observed principal dynamic balance for this section of the system. The accuracy of hydrodynamic predictions in the study area is demonstrated by comparison with four tidal elevation stations and two cross-section averaged current measurements. Simulated current is then used to model bed-load transport in the vicinity of a rapidly growing shoal located in the main channel of the lower system. Consisting of coarse sand and gravel, the shoal must be dredged every five to eight years. Two approaches are taken—an Eulerian parametric method in which nodal bed-load flux vectors are averaged over the tidal cycle and a Lagrangian particle tracking approach in which a finite number of sediment particles are released and tracked. Both methods yield pathways and accumulations in agreement with the observed shoal formation and the long-term rate of sediment accumulation in the shoal area.     

Investigating transport pathways in the ocean

The ocean is a very complex medium with scales of motion that range from thousands of kilometers to the dissipation scales. Transport by ocean currents plays an important role in many practical applications ranging from climatic problems to coastal management and accident mitigation at sea. Understanding transport is challenging because of the chaotic nature of particle motion. In the last decade, new methods have been put forth to improve our understanding of transport. Powerful tools are provided by dynamical system theory, that allow the identification of the barriers to transport and their time variability for a given flow. A shortcoming of this approach, though, is that it is based on the assumption that the velocity field is known with good accuracy, which is not always the case in practical applications. Improving model performance in terms of transport can be addressed using another important methodology that has been recently developed, namely the assimilation of Lagrangian data provided by floating buoys. The two methodologies are technically different but in many ways complementary. In this paper, we review examples of applications of both methodologies performed by the authors in the last few years, considering flows at different scales and in various ocean basins. The results are among the very first examples of applications of the methodologies to the real ocean including testing with Lagrangian in-situ data. The results are discussed in the general framework of the extended fields related to these methodologies, pointing out to open questions and potential for improvements, with an outlook toward future strategies.     

A modified Euler–Lagrange transformation for particle orbits in nonlinear progressive waves

This paper presents a modified Euler–Lagrange transformation method to obtain the third-order trajectory solution in a Lagrangian form for the water particles in nonlinear water waves. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness and an arbitrary vertical position for each water particle. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third-order asymptotic expressions for the Lagrangian particle trajectories, the mass transport velocity and the period of particle motion can be derived directly in Lagrangian form. The wave frequency and mean level of the particle motion in Lagrangian form differ from those of the Eulerian. Finally, the third-order asymptotic solution obtained is uniformly valid in contrast with early works containing resonant terms presented by Wiegel [1964. Oceanographical Engineering. Prentice-Hall, New Jersey, pp. 37–40] (Eqs. (B.1) and (B.1), (B.2) in Appendix B) or Chen et al.[2006. Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2 nonlinear waves. Wave motion, 43, 356–369] based on a straightforward expansion for two-dimensional progressive waves.     

厦门浔江海域污染扩散数值模拟

本文采用ＡＤＩ活动边界潮流数值模拟模拟了厦门浔江海域的潮流，计算的结果与实测数据比较吻合。文中用欧拉污染扩散数值模型计算了从同安、集美、五通口排出的污染物（ＣＯＤ）对浔江海域的影响，同时采用拉格朗日污染扩散数值模型研究在湾口、集美和在北部的湾顶污染物瞬时排放后的运移情况。     

Subtidal Flow Patterns in Western Florida Bay

Recent observations using moored current meters, shipboard ADCP transects, salinity mapping and drifters have been used to study the residual circulation including wind drift in western Florida Bay.Rapid, nearly synoptic surveys of salinity over a large area was an effective tracer-mapping technique, when salinity gradients were sufficiently strong, and provided qualitative information on Lagrangian water motion for the entire study area. The salinity maps indicated a general south-eastward advection, which was only subordinate to tidal mixing in a narrow zone adjacent to the Florida Keys.Drifter data collected simultaneously, allowed quantitative estimates to be added to the transport pattern suggested by salinity maps. The selectively deployed drifters yielded estimates of total drift velocities. In addition, moored current meters and shipboard current profiling were used to determine the distribution of flow across the mouth of the bay facing the Gulf of Mexico and the transport through Long Key Channel, a major connection between the bay and the Atlantic Ocean.Analysis showed that from 64 to over 92% of the drifter trajectory variances could be explained by the combination of a local wind drift, expressed in terms of a wind drift factor multiplied by the surface shear velocity, and an ambient current. For a 1 m high drifter deployed at the surface of the water column, the wind drift factor was found to be approximately 0·125m, making the drift speed roughly equal to 0·45% of wind speed. The mean drifter speeds were linearly proportional to mean transport estimates derived from the current meter observations in Long Key Channel, enhancing confidence in both data sets.The total south-eastward directed residual current varied between 100 and 5000 m day⁻¹and was weaker in summer than in winter, when southward winds associated with periodic passage of cold fronts boost the residual flow. The estimated contribution from local wind drift varied between 500 m day⁻¹in summer to 1000 m day⁻¹in winter. The remaining contribution to the observed Lagrangian residual circulation in western Florida Bay is caused by other forcing, including tidal rectification, remote wind forcing and large-scale current systems (the Gulf Stream and Florida Current systems).     

Particle trajectories of nonlinear gravity waves in deep water

The paper presents a numerical method for calculating the particle trajectories of nonlinear gravity waves in deep water. Particle trajectories, mass-transport velocity and Lagrangian wave period can be accurately determined by the proposed method. The high success rate of the proposed method is examined by comparing the present results with those of (a) Longuet-Higgins, M.S., 1986, 1987. Eulerian and Lagrangian aspects of surface waves. Journal of Fluid Mechanics 173, 683-707 and (b) Lagrangian moments and mass transport in Stokes waves. Journal of Fluid Mechanics 179, 547-555. It is shown that the dimensionless mass-transport velocity can exceed 10% for large waves, and the Lagrangian wave period is much larger than the Eulerian wave period for large waves.     

寒潮天气下高风险冰块追踪预测方法及数值模拟

为向拟建、在建和已建冰区所有冷源取水工程海域的海冰环境监测和动态风险预警提供技术支撑,本文构建了海冰–海洋耦合条件下的拉格朗日粒子追踪预测模型,并以辽东湾某核电站取水口为例,模拟并探讨了寒潮天气下高风险冰块在24 h、48 h和72 h的运移轨迹及其进入取水口的概率。结果表明,由于取水口的走向与流向和风向几乎垂直,因此在口门外随机释放的1 200个高风险冰块粒子中只有不到6%的粒子进入到取水口内。通过分区域标识粒子颜色,发现这些粒子多来自于靠近取水口300 m范围内。敏感性分析的结果表明,当释放粒子数量增至5倍时,结论不变。该项研究为冷源取水安全预警提供了一种新方法。