The mass transport velocity induced by free oscillations at a single frequency

Abstract

Second order effects due to the presence of a first order free oscillation at a single frequency in a variable depth rotating ocean are examined. It is found that the second order Lagrangian mean velocity (mass transport velocity) satisfies the linearized equations for unforced steady geostrophic motion. This implies that if the ocean basin is laterally bounded and contains no closed geostrophic contours, the second order Lagrangian mean velocity vanishes everywhere.     

Detecting surface geostrophic currents using wavelet filter from satellite geodesy

According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.     

基于卫星测高交叉点的海洋表面地转流速度

在流体静力平衡状态下,海洋Coriolis力和压力梯度平衡就形成地转流,世界上大多数海流都近似为地转流.本文利用卫星测高交叉点方法计算海洋表面地转流速度,分析了利用测高交叉点计算地转流速度的不确定性,上升和下降弧段的海面倾斜在分辨率50 km上可以达到10^-7量级,才可能获得优于10 cm/s的地转流速度.在低纬度或者纬度接近卫星轨道倾角的地区,由交叉点方法计算的地转流速度精度低于中纬度地区.以中国台湾东部黑潮为试验区,利用最新的中国台湾周边海域大地水准面模型参考场计算高精度的大地水准面高,利用TOPEX/Poseidon和Jason-1的GDR数据(2002~2005年)计算海面高,然后计算交叉点的动力高,确定交叉点的地转流速度,结果与中国台湾NCOR(National Center for Ocean Research)的流速基本一致.     

基于区域滤波的GOCE稳态海面动力地形和地转流

基于频域法,利用最新的GOCE卫星重力场模型和卫星测高数据计算了稳态海面动力地形.结合海洋表层漂流浮标的观测结果,对稳态海面动力地形进行了最优空间滤波尺度分析,给出了区域、纬度带和全球稳态海面动力地形的最优空间滤波尺度因子.在此基础上,给出了全球和区域地转流.结果表明:在中高纬度和全球区域,可以分别获得空间尺度优于102km和127km的稳态海面动力地形信息.与海洋表层漂流浮标对比可知,在强流区域,采用稳态海面动力地形得到的地转流速可以解释观测浮标流速的70%;在中高纬度区域,由GOCE重力场得到的地转流略优于对应的GRACE结果;在近赤道区域,由GOCE重力场得到的地转流精度略低于对应的GRACE结果;在北大西洋和阿古拉斯强流区域,由GOCE得到的地转流场明显优于对应的GRACE结果,其精度分别提高了16%和24%.     

Geostrophic currents in shelf areas

A method for obtaining geostrophic currents in a stratified ocean is discussed. It combines the use of hydrographic data and numerical modelling. For geostrophic flow in a flatbottom stratified ocean it is shown along the lines of Gill and Clarke (1974, Deep-Sea Research, 21, 325–345) that the surface elevation is determined by the barotropic mode. Experience indicates strongly that this also is the case when the depth varies. Hence the surface elevation, or equivalently the surface velocity, can be obtained from the depth-averaged equations.The variation with depth of the current is determined from hydrographic measurements, assuming that the baroclinic field is in geostrophic balance. When integrating in the vertical, the velocity at the sea surface obtained from the numerical computations is used as an absolute reference velocity.The method has been applied to the flow in the Faroe-Shetland Channel using meteorological data for the atmospheric forcing. The field data are from Foldvik andKvinge (1975), and were collected during ‘Overflow—1973’. The computations were performed for one particular wind event associated with an atmospheric low pressure passage. We find a net flux of 2.9 Sv of Atlantic water into the Norwegian Sea for the considered period of time. At the bottom of the channel there was a flow of 0.7 Sv of Norwegian Sea water into the Atlantic in the same period. On examining our calculated vertical velocity profiles in the channel, we find a level of zero motion which is not far from the position of the 35‰ isohaline. These results are discussed in connection with long-time average fluxes reported elsewhere in the literature.     

On the theory of thin rotating jets: A quasi‐geostrophic time dependent model

The time‐dependent meandering in a thin baroclinic jet over bottom topography is discussed in the quasi‐geostrophic approximation. The motion of the axis of the jet is taken to be vertically coherent and the axis itself is defined as inextensible. The motion is examined from a frame of reference moving with the axis but fixed at an arbitrary longitude in terms of an open ocean spatial initial value problem. The velocities of the axis and of the jet are quasi‐geostrophic, and vorticity conservation for the first non‐geostrophic components constrains the evolution of the axis and gives a path equation. The spatial linearized stability problem is studied and the jet is found to be baroclinically unstable to path disturbances of sufficiently high frequency which amplify downstream. An exact solution is obtained to the nonlinear path equation over a flat bottom with no ß‐effect. The evolution of the path of these unstable meanders is such that the path closes itself and forms rings (at which point the analysis breaks down). It is proposed that the baroclinic jet processes studied here are fundamental to the dynamics of Gulf Stream meandering and isolated eddy production.     

Dispersion of passive tracers in model flows: effects of the parametrization of small-scale processes

A set of numerical experiments is presented, in which we study the dynamics of passive particles advected by given two-dimensional velocity fields and perturbed by a non-white noise with a characteristic time . Data and model results have shown that this kind of random perturbation is able to represent subgridscale processes for upper ocean mesoscale turbulence for regions of the world ocean where turbulence can be assumed to be homogeneous. Extensive computations in different fields characterized by cell-like structure, both stationary and time-dependent, representing very idealized geophysical flow situations, show that the presence of a finite correlation time scale does lead to enhanced or arrested dispersion, depending on the considered flow; however, it does not seem to affect the gross qualitative behaviour of the dispersion processes, which is primarily affected by the large-scale velocity field.     

Geophysical flows under location uncertainty,Part III SQG and frontal dynamics under strong turbulence conditions

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. This change can be consistently applied to all fluid dynamics evolution laws. This paper continues to explore benefits of this framework and consequences of specific scaling assumptions. Starting from a Boussinesq model under location uncertainty, a model is developed to describe a mesoscale flow subject to a strong underlying submesoscale activity. Specifically, turbulent diffusion and rotation effects have similar orders of magnitude. As obtained, the geostrophic balance is modified and the Quasi-Geostrophic assumptions remarkably lead to a zero Potential Vorticity. The ensuing Surface Quasi-Geostrophic model provides a simple diagnosis of warm frontolysis and cold frontogenesis.     

The relation between the mean vector surface wind and the mean vector pressure gradient over the oceans

Summary Mean values of the angle of inclination between the mean vector surface wind and the mean isobars have been calculated as a function of latitude for a number of independent Marsden squares over the ocean. Mean values of the ratio between the mean vector surface wind velocity and the calculated geostrophic wind velocity have been computed in the same way. Some general inferences about the general circulation have been drawn from the results.     

Three‐dimensional non‐geostrophic disturbances in a baroclinic zonal flow

Abstract

A study is made to determine the stability properties of a baroclinic zonal current on which small amplitude three‐dimensional non‐geostrophic disturbances are superimposed. The flow is assumed to be bounded to the north and south by rigid vertical walls and the Rossby number Ro is taken to be small compared to unity. It is then shown that if the perturbation quantities are expanded in power series in Ro the leading or zero order terms in the series correspond to the quasi‐geostrophic solution obtained by Eady (1949) and that the higher order terms represent the “non‐geostrophic” effects neglected by the latter.

It is shown that to the second order in Ro the non‐geostrophic effects decrease the growth rates of those disturbances which are found to be unstable according to Eady's analysis but do not alter their speed of propagation. The results indicate, on the other hand, that to the same order of approximation the stable waves travel at a speed which is different from that given by Eady's solution. The modification of the perturbation wave structure by the non‐geostrophic effects is also investigated. It is found in particular that to the first order in Ro the latter produce a northward tilt with height in the ridge (or trough) lines of the meridional and vertical particle velocity fields away from the lateral boundaries.     

On the basic structure of oceanic gravity currents

Results from numerical simulations of idealised, 2.5-dimensional Boussinesq, gravity currents on an inclined plane in a rotating frame are used to determine the qualitative and quantitative characteristics of such currents. The current is initially geostrophically adjusted. The Richardson number is varied between different experiments. The results demonstrate that the gravity current has a two-part structure consisting of: (1) the vein, the thick part that is governed by geostrophic dynamics with an Ekman layer at its bottom, and (2) a thin friction layer at the downslope side of the vein, the thin part of the gravity current. Water from the vein detrains into the friction layer via the bottom Ekman layer. A self consistent picture of the dynamics of a gravity current is obtained and some of the large-scale characteristics of a gravity current can be analytically calculated, for small Reynolds number flow, using linear Ekman layer theory. The evolution of the gravity current is shown to be governed by bottom friction. A minimal model for the vein dynamics, based on the heat equation, is derived and compares very well to the solutions of the 2.5-dimensional Boussinesq simulations. The heat equation is linear for a linear (Rayleigh) friction law and non-linear for a quadratic drag law. I demonstrate that the thickness of a gravity current cannot be modelled by a local parameterisation when bottom friction is relevant. The difference between the vein and the gravity current is of paramount importance as simplified (streamtube) models should model the dynamics of the vein rather than the dynamics of the total gravity current. In basin-wide numerical models of the ocean dynamics the friction layer has to be resolved to correctly represent gravity currents and, thus, the ocean dynamics.     

Improving Surface Geostrophic Current from a GOCE-Derived Mean Dynamic Topography Using Edge-Enhancing Diffusion Filtering

With increased geoid resolution provided by the gravity and steady-state ocean circulation explorer (GOCE) mission, the ocean’s mean dynamic topography (MDT) can be now estimated with an accuracy not available prior to using geodetic methods. However, an altimetric-derived MDT still needs filtering in order to remove short wavelength noise unless integrated methods are used in which the three quantities are determined simultaneously using appropriate covariance functions. We studied nonlinear anisotropic diffusive filtering applied to the ocean´s MDT and a new approach based on edge-enhancing diffusion (EED) filtering is presented. EED filters enable controlling the direction and magnitude of the filtering, with subsequent enhancement of computations of the associated surface geostrophic currents (SGCs). Applying this method to a smooth MDT and to a noisy MDT, both for a region in the Northwestern Pacific Ocean, we found that EED filtering provides similar estimation of the current velocities in both cases, whereas a non-linear isotropic filter (the Perona and Malik filter) returns results influenced by local residual noise when a difficult case is tested. We found that EED filtering preserves all the advantages that the Perona and Malik filter have over the standard linear isotropic Gaussian filters. Moreover, EED is shown to be more stable and less influenced by outliers. This suggests that the EED filtering strategy would be preferred given its capabilities in controlling/preserving the SGCs.     

High-order schemes for 2D unsteady biogeochemical ocean models

Accurate numerical modeling of biogeochemical ocean dynamics is essential for numerous applications, including coastal ecosystem science, environmental management and energy, and climate dynamics. Evaluating computational requirements for such often highly nonlinear and multiscale dynamics is critical. To do so, we complete comprehensive numerical analyses, comparing low- to high-order discretization schemes, both in time and space, employing standard and hybrid discontinuous Galerkin finite element methods, on both straight and new curved elements. Our analyses and syntheses focus on nutrient–phytoplankton–zooplankton dynamics under advection and diffusion within an ocean strait or sill, in an idealized 2D geometry. For the dynamics, we investigate three biological regimes, one with single stable points at all depths and two with stable limit cycles. We also examine interactions that are dominated by the biology, by the advection, or that are balanced. For these regimes and interactions, we study the sensitivity to multiple numerical parameters including quadrature-free and quadrature-based discretizations of the source terms, order of the spatial discretizations of advection and diffusion operators, order of the temporal discretization in explicit schemes, and resolution of the spatial mesh, with and without curved elements. A first finding is that both quadrature-based and quadrature-free discretizations give accurate results in well-resolved regions, but the quadrature-based scheme has smaller errors in under-resolved regions. We show that low-order temporal discretizations allow rapidly growing numerical errors in biological fields. We find that if a spatial discretization (mesh resolution and polynomial degree) does not resolve the solution, oscillations due to discontinuities in tracer fields can be locally significant for both low- and high-order discretizations. When the solution is sufficiently resolved, higher-order schemes on coarser grids perform better (higher accuracy, less dissipative) for the same cost than lower-order scheme on finer grids. This result applies to both passive and reactive tracers and is confirmed by quantitative analyses of truncation errors and smoothness of solution fields. To reduce oscillations in un-resolved regions, we develop a numerical filter that is active only when and where the solution is not smooth locally. Finally, we consider idealized simulations of biological patchiness. Results reveal that higher-order numerical schemes can maintain patches for long-term integrations while lower-order schemes are much too dissipative and cannot, even at very high resolutions. Implications for the use of simulations to better understand biological blooms, patchiness, and other nonlinear reactive dynamics in coastal regions with complex bathymetric features are considerable.     

有限元三角网格中波动的频散分析及数值仿真

波动问题有限元离散后会引起数值误差, 数值频散的本质就是数值误差传播引起的非物理解. 数值频散不仅没有实际意义, 而且还会影响对真实波动现象的认识. 为厘清有限元三角网格中波动数值频散的影响因素, 本文推导了集中质量矩阵和一致质量矩阵的频散函数, 同时给出了组合质量矩阵的频散函数, 并对不同质量矩阵的数值频散进行了对比研究. 理论分析和数值计算结果表明: 有限元三角网格中波动的数值频散受网格布局、 波传播方向、 单元网格纵横比以及质量矩阵的影响; 一致质量矩阵的数值频散比集中质量矩阵更易受到波传播方向的影响; 不合理的三角网格单元会对数值相速度(数值频散)产生不良影响; 正三角网格中波动的数值频散几乎不受波传播方向的影响; 一致质量矩阵与集中质量矩阵的线性组合能够有效地压制数值频散.      

Lateral stirring of large-scale tracer fields by altimetry

Ocean surface fronts and filaments have a strong impact on the global ocean circulation and biogeochemistry. Surface Lagrangian advection with time-evolving altimetric geostrophic velocities can be used to simulate the submesoscale front and filament structures in large-scale tracer fields. We study this technique in the Southern Ocean region south of Tasmania, a domain marked by strong meso- to submesoscale features such as the fronts of the Antarctic Circumpolar Current (ACC). Starting with large-scale surface tracer fields that we stir with altimetric velocities, we determine ‘advected’ fields which compare well with high-resolution in situ or satellite tracer data. We find that fine scales are best represented in a statistical sense after an optimal advection time of ～2 weeks, with enhanced signatures of the ACC fronts and better spectral energy. The technique works best in moderate to high EKE regions where lateral advection dominates. This technique may be used to infer the distribution of unresolved small scales in any physical or biogeochemical surface tracer that is dominated by lateral advection. Submesoscale dynamics also impact the subsurface of the ocean, and the Lagrangian advection at depth shows promising results. Finally, we show that climatological tracer fields computed from the advected large-scale fields display improved fine-scale mean features, such as the ACC fronts, which can be useful in the context of ocean modelling.     

层结稳定性“豁口”与北太平洋副热带中部模态水形成机制

本文首先指出北太平洋副热带中部模态水（简称中部模态水）的形成具有显著的“局地”特征,其形成海区在（165°E～160°W,38°N～42°N）区间. 海气通量分析表明单纯的外部大气强迫场（太阳短波辐射、净热通量和风应力旋度）不能解释中部模态水形成海区的“局地”性;进一步对上层海洋层结季节变化特征的分析发现秋季（9～10月）在北太平洋中部上层海洋（<75 m）（165°E～160°W,38°N～42°N）区间存在特殊的浮力频率低值区——层结稳定性“豁口”. 该层结稳定性“豁口”作为“预条件（Precondition Mechanism）”机制对中部模态水形成的“局地”特征给出了合理的解释. 在上述研究的基础上,基于一个上层海洋混合层热平衡方程,通过诊断分析揭示该层结稳定性“豁口”是由海表热力强迫、垂向挟卷、Ekman平流和地转平流效应共同导致的,“豁口”东、西边界的确定直接或间接地取决于海表热力强迫、Ekman冷平流和地转暖平流的纬向分布差异.     

Mechanisms of metal–silicate equilibration in the terrestrial magma ocean

It has been proposed that the high concentrations of moderately siderophile elements (e.g. Ni and Co) in the Earth’s mantle are the result of metal–silicate equilibration at the base of a deep magma ocean that formed during Earth’s accretion. According to this model, liquid metal ponds at the base of the magma ocean and, after equilibrating chemically with the overlying silicate liquid at high pressure (e.g. 25–30 GPa), descends further as large diapirs to form the core. Here we investigate the kinetics of metal–silicate equilibration in order to test this model and place new constraints on processes of core formation. We investigate two models: (1) Reaction between a layer of segregated liquid metal and overlying silicate liquid at the base of a convecting magma ocean, as described above. (2) Reaction between dispersed metal droplets and silicate liquid in a magma ocean. In the liquid-metal layer model, the convection velocity of the magma ocean controls both the equilibration rate and the rate at which the magma ocean cools. Results indicate that time scales of chemical equilibration are two to three orders of magnitude longer than the time scales of cooling and crystallization of the magma ocean. In the falling metal droplet model, the droplet size and settling velocity are critical parameters that we determine from fluid dynamics. For likely silicate liquid viscosities, the stable droplet diameter is estimated to be ∼1 cm and the settling velocity ∼0.5 m/s. Using such parameters, liquid metal droplets are predicted to equilibrate chemically after falling a distance of <200 m in a magma ocean. The models indicate that the concentrations of moderately siderophile elements in the mantle could be the result of chemical interaction between settling metal droplets and silicate liquid in a magma ocean but not between a segregated layer of liquid metal and overlying silicate liquid at the base of the magma ocean. Finally, due to fractionation effects, the depth of the magma ocean could have been significantly different from the value suggested by the apparent equilibration pressure.     

Tide model comparison over the Southwestern Atlantic Shelf

Sea surface height (SSH) as measured by satellites has become a powerful tool for oceanographic and climate related studies. Whereas in the open ocean good accuracy has been achieved, more energetic dynamics and a number of calibration problems have limited applications over continental shelves and near the coast. Tidal ranges in the Southwestern Atlantic (SWA) continental shelf are among the highest in the world ocean, reaching up to 12 m at specific locations. This fact highlights the relevance of the accuracy of the tidal correction that must be applied to the satellite data to be useful in the region. In this work, amplitudes and phases of tidal constituents are extracted from five global tide models and three regional models and compared to the corresponding harmonics estimated from coastal tide gauges (TGs) and satellite altimetry data. The Root Sum Square (RSS) of the misfit of the common set of the five tidal constituents solved by the models (M₂, N₂, S₂, K₁ and O₁) is higher than 18 cm close to the coast for two of the regional models and higher than 24.5 cm for the rest of the models considered. Both values are too high to provide an accurate estimation of geostrophic non-tidal currents from satellite altimetry in the coastal region. On the other hand, the global model with the highest spatial resolution has a RSS lower than 4.5 cm over the continental shelf even when the non-linear M₄ overtide is considered. Comparison with in-situ current measurements suggests that this model can be used to de-tide altimetry data to compute large-scale patterns of SSH and associated geostrophic velocities. It is suggested that a local tide model with very high resolution that assimilates in-situ and satellite data should meet the precision needed to estimate geostrophic velocities at a higher resolution both close to the coast and over the Patagonian shelf.     

Convection in a rotating magnetic system and Taylor's constraint

Abstract

A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects.     

On a generalized potential vorticity equation for quasi-geostrophic flow

Summary It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number.