Dispersion of passive tracers and finite-scale Lyapunov exponents in the Western Mediterranean Sea

A realistic 4-year dataset of the surface velocity field of the western Mediterranean Sea obtained with the Mediterranean Forecasting System and the GFDL-MOM model was used to obtain the finite-scale Lyapunov exponents (FSLE) and finite-size diffusion coefficients. Dispersive properties and Lagrangian parameters in four sub-basins are discussed, and a comparison is made between the FSLE and the Eulerian Okubo–Weiss parameter obtained for the same area with the same dataset. An additional comparison is made with the FSLE calculated from independent datasets obtained from 15 drifters launched in the Algerian basin during October of 1996.     

The reduction of plankton biomass induced by mesoscale stirring: A modeling study in the Benguela upwelling

Recent studies, both based on remote sensed data and coupled models, showed a reduction of biological productivity due to vigorous horizontal stirring in upwelling areas. In order to better understand this phenomenon, we consider a system of oceanic flow from the Benguela area coupled with a simple biogeochemical model of Nutrient-Phyto-Zooplankton (NPZ) type. For the flow three different surface velocity fields are considered: one derived from satellite altimetry data, and the other two from a regional numerical model at two different spatial resolutions. We compute horizontal particle dispersion in terms of Lyapunov exponents, and analyzed their correlations with phytoplankton concentrations. Our modeling approach confirms that in the south Benguela there is a reduction of biological activity when stirring is increased. Two-dimensional offshore advection and latitudinal difference in primary production, also mediated by the flow, seem to be the dominant processes involved. We estimate that mesoscale processes are responsible for 30–50% of the offshore fluxes of biological tracers. In the northern area, other factors not taken into account in our simulation are influencing the ecosystem. We suggest explanations for these results in the context of studies performed in other eastern boundary upwelling areas.     

基于拉格朗日分析法的中尺度涡精细三维结构研究及其误差估计

在前人的工作中，拉格朗日分析法被用来演示大尺度环流，同时拉格朗日拟序结构可以较好的演示中尺度涡两维结构的发展过程。然而，很少研究关注怎么利用拉格朗日分析法针对中尺度涡三维结构进行演示。与以往利用欧拉方法研究中尺度涡三维结构的工作不同，我们利用拉格朗日分析法，从另一个视角来研究涡旋结构。我们在海山上方模拟出一个理想的气旋涡，涡旋内的下沉流和涡旋旁的上升流形成一个闭合的环流。这种结构很难从欧拉角度来演示。然而，粒子的运动轨迹很好地展示了整个循环:流体在涡旋中旋转下沉，汇聚到底层的上升流区，并通过上升流返回到海表面。我们也将拉格朗日分析法应用于真实的模拟结果中。作为中国南海的一个重要现象，靠近越南中部的海域中的偶极子（反气旋涡/气旋涡），关于其结构的研究已经比较成熟了，但这些研究主要关注的是海面过程。通过拉格朗日分析，我们很好的演示了偶极子的三维结构:流体在反气旋涡(气旋涡)内部旋转上升(下沉)。更重要的是，粒子的轨迹表明，这两个涡旋之间不存在水团交换，因为强边界急流将它们彼此分开。以上结论均得到了计算误差估计的可信度支持。尽管在强辐散流和强垂直扩散流中，计算误差逐渐增大，但是在一定的时间步长和积分周期内，计算误差始终保持在一个较小的值。     

How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics?

Much of atmospheric and oceanic transport is associated with coherent structures. Lagrangian methods are emerging as optimal tools for their identification and analysis. An important Lagrangian technique which is starting to be widely used in oceanography is that of finite-size Lyapunov exponents (FSLEs). Despite this growing relevance there are still many open questions concerning the reliability of the FSLEs in order to analyse the ocean dynamics. In particular, it is still unclear how robust they are when confronted with real data. In this paper we analyze the effect on this Lagrangian technique of the two most important effects when facing real data, namely noise and dynamics of unsolved scales. Our results, using as a benchmark data from a primitive numerical model of the Mediterranean Sea, show that even when some dynamics is missed the FSLEs results still give an accurate picture of the oceanic transport properties.     

Numerical modelling of Lagrangian residual current in the Bohai Strait

The Bohai Strait is the only passage-way of the semienclosed Bohai Sea into the outer ocean. The various dynamical processes have great effects on both sides of the strait, especially on the Bohai Sea. Tidal current dominates in the strait, and among the tida! components the M, component tide is prevailing.The seawater in the strait is homogeneous vertically almost the whole year because of strong tidal mixing. The M, component tide was simulated numerically using two dimensional barotropical model, and the Eulerian tide-induced residual currents were also deduced. The results showed that the tidal currents were dominated by the coastal line and topography. There exist many eddies in the tide-induced residual current fields, particularly near the northern coast.On the basis of the simulation of the tidal currents, the movements of the water particles in the strait were tracked by means of Lagrangian techniques. Consequently the Lagrangian residual currents were obtained. Somewhat similar to the Eulerian     

Lagrangian analysis of mixing and transport of water masses in the marine bays

The Lagrangian approach to studying the mixing and transport of a passive admixture in marine bays and gulfs based on the methods of a theory of dynamic systems is developed. This approach is employed to investigate the lateral mixing and transport of waters in the Peter the Great Bay, Japan Sea, using a velocity field of the predictive numerical hydrodynamic circulation model of a synoptic scale. It is shown that the Lagrangian characteristics, such as the maximum accumulated Lyapunov exponent, the time of particle stay in the bay, particle relative displacements, and the number of cyclonic and anticyclonic rotations, allow us to describe the movement of water masses, the character of mixing, and chaos in the Bay. In integrating the advection equations forward and backward in time, maps showing a number of particle arrivals to different regions of the Bay make it possible to establish corridors through which particles leave and enter the Bay.     

A Lagrangian mean theory on coastal sea circulation with inter-tidal transports I. Fundamentals

A brief review is made on the theory of the Lagrangian residual circulation and inter-tidal transports in a convectively weakly nonlinear system. In the review the emphasis is put on the systematical development of the theory and its weakness of convectively weakly nonlinear approximation. The fundamentals of a Lagrangian tidally-averaged theory on circulation with inter-tidal transport processes have been proposed for a general nonlinear coastal/estuarine system. The Lagrangian residual velocity is strictly de- fined, and it has been verified to be able to embody the velocity field of circulation. A new concept of the concentration for inter- tidal transport processes is presented. The concentration describing the inter-tidal transport processes should be a ＂Lagrangian inter-tidal concentration＂ defined and named, but not the Eulcrian tidally-averaged concentration used traditionally. The circulation described here contains a set of infinite temporal-spatial fields of velocity/concentration, each of which corresponds to a specific value of tidal phases varying continuously over one tidal cycle. When the convectively weakly nonlinear condition（ with a smaller order of eddy diffusion and sources） is approximately satisfied, a set of infinite temporal-spatial fields of velocity/concentration can be reduced to a single one.. the mass transport velocity/the Eulerian tidally averaged concentration as exhibited traditionally.     

有限尺度李雅普诺夫指数与海表温度梯度相关性的初步分析

为了探究海表温度和海面高度之间的瞬时相关性,介绍了一种卫星测高数据的拉格朗日分析指数--有限尺度李雅普诺夫指数(Finite Size Lyapunov Exponent,FSLE),以黑潮延伸体区域的涡旋和南大西洋的亚南极锋为例,通过对观测、模式结果和融合产品结果的分析,探讨了该指数与海表温度梯度(Sea Surface Temperature Gradient,SSTG)之间的相关性。比较FSLE图像和SSTG图像发现,FSLE与SSTG均呈丝状结构,对海洋表层水体结构描述具有一致性,尤其在温度梯度大和地转流强的区域更为一致。二者的一致性要远好于其他常用方式,比如全流速、OW参数涡旋识别方法和Winding-Angle涡旋识别方法。不同区域FSLE与SSTG之间的相关性表现不同,黑潮延伸体区域相关系数存在显著的季节变化,而南大西洋亚南极锋区域季节内变化突出。     

健康人与心脏病人心电信号混沌特性比较研究

Lyapunov指数是混沌理论的重要参数之一,对分析心电信号特性有重要意义。分别计算健康人和3种心脏病人心电信号的Lyapunov指数,并首次采用室上病变病人作为样本进行研究。对比发现健康人与各类心脏病人的Lyapunov指数之间存在显著差别。同时在重构相空间过程中采用1种同时估计延迟时间τ和嵌入维数m的新方法,并与自相关函数法的计算结果进行对比,在二维相空间重构图上进行验证。结果表明这种方法优于自相关函数法。     

Lagrangian Transport by Currents Variable in Time in the Model of Wind-Induced Circulation of the Black Sea

We construct a simple model of seasonal variability of circulation in the Black Sea, which satisfactorily explains the data of altimetric satellite observations. The model is used to describe the nonstationary wind-induced currents in a round basin and study the trajectories of water particles in the surface layer of the sea. It is shown that, for nonstationary currents, these trajectories can be quite complicated. It is also assumed that Lagrangian mixing can be caused by the complex trajectories of water particles.     

Seasonal variation of atmospheric coupling with oceanic mesoscale eddies in the North Pacific Subtropical Countercurrent

This study investigated the seasonal variation in the atmospheric response to oceanic mesoscale eddies in the North Pacific Subtropical Countercurrent (STCC) and its mechanism, based on satellite altimetric and reanalysis datasets. Although mesoscale eddy in the study area is more active in summer, the sea surface temperature (SST) anomaly associated with mesoscale eddies is more intense and dipolar in winter, which is largely due to the larger background SST gradient. Similarly, the impact of the oceanic eddy on sea surface wind speed and heat flux is strongest in winter, whereas its effect on precipitation rate is more significant in summer. The study revealed that the SST gradient in STCC could impact the atmosphere layer by up to 800 hPa (900 hPa) in boreal winter (summer) through the dominant vertical mixing mechanism. Moreover, the intensity of the SST gradient causes such seasonal variation in mesoscale air-sea coupling in the study region. In brief, a stronger (weaker) background SST gradient field in wintertime (summertime) leads to a larger (smaller) eddy-induced SST anomaly, thus differently impacting atmosphere instability and transitional kinetic energy flux over oceanic eddies, leading to seasonal variation in mesoscale air-sea coupling intensity.     

Energetics of lateral eddy diffusion/advection：Part Ⅱ. Numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion

Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and ad vection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial hori zontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models; therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with hori zontal advection in the commonly used Eulerian coordinates may become one of the most challenging ob stacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion （mixing） has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps： stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.     

Identification and Lagrangian analysis of oceanographic structures favorable for fishery of neon flying squid (<Emphasis Type="Italic">Ommastrephes bartramii</Emphasis>) in the South Kuril area

Based on the AVISO velocity field, we compute daily synoptic Lagrangian maps in the South Kuril area for the fishery seasons of 1998, 1999, and 2001–2005 from available catching data on neon flying squid (NFS). With the help of drift maps for artificial particles, we found that the majority of NFS fishing grounds featuring maximum catches are situated near large-scale Lagrangian intrusions: tongues of water penetrating the surrounding water of other Lagrangian properties. It is shown that the NFS catch locations tend to accumulate at places where waters with different magnitudes of certain Lagrangian indicators converge, mix, and produce filaments, swirls, and tendrils typical of chaotic advection. Potential NFS fishing grounds are mainly located near (1) Lagrangian intrusions of the Subarctic front, (2) intrusions of Okhotsk Sea and Oyashio waters around mesoscale anticyclones east of Hokkaido with subsequent penetration of catch locations inside eddies and (3) intrusions of subtropical waters into the central part of the South Kuril area due to interaction with eddies of different size and polarity. Possible reasons for increased biological production and fishery in the vicinity of Lagrangian intrusions are discussed.     

冰动力学的拉格郎日离散元模式

本文描述一种应用于河冰和海冰动力学研究的平滑质点流体力学的离散元模式。该离散元方法是一种自由拉格郎日方法,和传统的欧拉网格数值方法相比,它具有较小的数值扩散并且能够更加灵活地处理复杂的冰过程等许多优点。本文首先给出海冰动力学的离散元模式的基本方法,并与欧拉有限差分方法和半拉格郎日的质点一网格方法进行了对比,其次,本文还给出了离散元海冰模式在渤海的一个应用。     

现场海域水平扩散系数的探讨

根据Taylor的扩散理论,按Hay和Pasquill的拉格朗日流与欧拉流自相关函数相似的假定,用实测的长序列欧拉流资料,计算了不同时间尺度的水平扩散系数。     

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.     

Energetics of lateral eddy diffusion/advection：Part Ⅳ. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.     

Comments on the “shear effect” and diffusion in the Lagrangian framework

We indentify three different types of Lagrangian coordinate systems that are used in oceanography. These are: true Lagrangian coordinates (TLC), Lagrangian coordinates (LC), and averaged Lagrangian coordinates (ALC). The diffusion process is studied in each of these coordinate systems. At large scales the eddydiffusivity is proven to be independent of molecular diffusivity, providing the spectrum of turbulent kinetic energy varies as scale raised to a power less than 4 1/3. The shear effect is examined using solutions to the averaged Lagrangian diffusion equation obtained by Okuboet al. (1983). In Eulerian coordinates both advection and diffusion are necessary for the occurrence of the shear effect, while in ALC timedependent dispersion coefficients are necessary for the process. In TLC we use the method of Taylor (1921) to study the dispersion of material by a velocity field, that from the Eulerian perspective, consists of turbulent motion across a uniform shear. The transformation of the above Eulerian velocity field into TLC results in a uniform deformation field and turbulent motion both along and across the shear. This work shows how dispersion of material is related to the turbulent Eulerian velocity and uniform velocity gradients. The instantaneous rate of change of variance of a spreading patch of material is completely specified by the instantaneous divergence obtained over the area occupied by the patch (Kawai, 1976). This relationship is shown to depend upon the fact that at any particular instant it is possible to define TLC that are equivalent to the Eulerian coordinates. In order to describe patch spreading from divergence measured over longer periods it is also necessary to consider other dispersive processes.Contribution number of the Newfoundland Institute of Cold Ocean Science.     

Phytoplankton patchiness: the role of lateral stirring and mixing

Explanations for the patchy distribution of marine phytoplankton are critically reviewed with the focus on the role played by lateral advection and mixing. Generating mechanisms for what is increasingly seen as a ubiquitous feature of the oceans have been sought in biology, behaviour, population dynamics, physics and various combinations thereof. As the mesoscale and sub-mesoscale (1-500 km) contain the “weather” of the ocean—eddies and fronts capable of strong stirring and mixing of any tracers advected by them—the physical circulation in this regime may have a strong role in the generation of patchiness. As a consequence, the focus here is on the ways the turbulent currents at these scales can interact with other processes to produce the complex spatial structures in phytoplankton distributions seen in countless satellite images and cruise data. The mechanisms reviewed include patch formation (KiSS theory), filamentation, Turing and related instabilities, diffusion waves, shear effects and turbulent stirring. Parallel to this is a discussion of observations and of the techniques that have been used to analyse them, particularly spectral analysis. It will be seen that many of the limitations in extant theories stem from a paucity of data and ambiguity in its interpretation. A synthesis of recent developments in sampling, instrumentation, image analysis and turbulence theory is used to suggest alternatives to conventional approaches, to highlight important work in related fields and to motivate new lines of research.     

季风环流影响下的南海海洋细菌多样性特征初探

季风驱动下的南海海洋动力过程有着季节性的多尺度变化特征, 显著影响南海海洋生态系统的演化进程。海洋细菌作为海洋生态系统中物质循环和能量流动的重要组成部分, 对环境变化和海洋多尺度动力过程有着积极的响应。将微生物生态过程与海洋动力过程相结合, 研究微生物的群落结构、动态变化及其与海洋环境过程的耦合, 是目前国际海洋科学多学科交叉研究的热点之一。文章以国家自然科学基金重点项目“季风环流影响下的南海海洋细菌多样性特征及其生物海洋学意义”的主要研究成果为基础, 从南海北部上升流、海洋锋面、中尺度涡旋、次中尺度过程及其对海洋细菌多样性和生态系统可能的影响等几个方面, 探讨当前的研究进展和初步研究成果。