f-平面中尺度海盆热力驱动边界流的形成

采用一个f-平面准地转但未作线性化假定的惯性模型, 考虑了西侧固壁附近摩擦层的作用, 在热量守恒条件下, 研究了理想化的长方体海盆区域内的扰动温度、边界急流及上升(下沉)流. 设研究区域上表面有净的热量输入, 相应的西侧边界有等量的热量耗散, 其余边界与外界无热量交换, 从而整个海域海水热量守恒. 结果表明, 在西侧边界扰动温度密集出现温度锋; 扰动压力及流场存在上下层翻转现象, 下层西侧为向北的沿岸急流, 扰动压力极大值中心位于西部, 上层东侧为向南的急流, 扰动压力极大值中心位于东部. 西侧较窄的范围内出现较强的垂向流, 中部区域也有较大的垂向运动. 文中还研究了不同形式的上表面热力强迫的影响, 结果表明对于不同形式的上边界热力强迫, 均可在海盆西侧出现扰动温度密集, 边界急流, 亦有上下层流场的翻转现象, 但垂向流的分布则有很大不同.     

准地转大洋风生环流的格子Boltzmann数值模拟

建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征. 此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.     

热带半地转适应过程

在热带地区,当纬圈或经圈方向上的地转平衡遭到破坏后,非地转运动将激发出重力惯性波,随着重力惯性波的频散,纬圈或经圈方向的地转平衡将重新建立,且遵循半位势涡度不变式.对半位势涡度不变式的讨论指出,纬圈或经圈半地转适应过程的方向主要依赖于初始扰动的经圈特征尺度.对于纬(经)圈半地转适应运动来说,只要初始扰动的纬圈特征尺度足够大(小),则适应场的特点总是压力场和纬(经)圈流的相互适应.     

南海季风性海流的建立与调整

通过一个高分辨(1/6度×1/6度)南海环流模式, 在旋转加快(spin-up)过程中分析了南海上层海洋季风驱动下海盆尺度环流特征建立的方式与内在机制, 分析了南海自静止态至海盆尺度环流特征初步形成的过程, 揭示了此过程中边界截获Kelvin波和西传斜压Rossby波的重要作用, 由此估算了南海上层海洋季风性海流调整的特征时间尺度.     

南极绕极流及经圈翻转流的双平衡态理论

利用非线性惯性理论研究南极绕极流及其经圈环流.模型分为上下两层,上层为Ekman层,主要由海表风应力驱动;下层为温跃层,其运动由理想流体的非线性方程控制.通过确定普适函数的形式求得温跃层中惯性模型的解.计算结果表明,在上层条件不变的情况下,温跃层存在两个平衡态解.平衡态1的流函数分布较为平滑,经圈环流深度较浅,纬圈流强度较小;平衡态2的流函数会出现不连续的状况,经圈环流可达2000m深,纬圈流的强度要比平衡态1大.两个平衡态中纬圈流在温跃层中均存在一个大值区.理论结果特别是平衡态2的结果与资料较为接近.     

基于准地转垂直运动方程对Q矢量的进一步探讨

Q矢量是诊断大气大尺度垂直运动的重要物理量.在f平面近似下,从原始运动方程组出发可以推导出Q矢量以及相关的半地转Q矢量、非地转Q矢量和湿Q矢量等表达式,但这种传统的推导方法没有考虑大气准地转运动的属性.本文利用数学物理变换,直接从准地转ω方程出发推导出Q矢量及其相关表达式,从而克服了传统方法在大气准地转运动属性表达方面...     

海浪波生切应力及其对流驱动作用的估计

依据 f 平面近似下线化无粘流体运动方程的一般形式, 并考虑地转角速度水平分量的作用, 首次给出真正地转意义下均匀水底上的小振幅波动解. 由此解导出的波生切应力包括波向与横向两个分量, 但其一阶近似即为Hasselmann和ZhiGang Xu等给出的结果. 文中还依地转波生应力和Longuet-Higgins等人提出的虚拟波生应力(virtual wave stress)计算了海面上波生总应力与风应力的比值, 估计了该应力在我国海域环流研究中的重要性, 强调在我国渤、黄海环流研究中考虑海浪的驱动作用的必要性.     

三维逆时偏移GPU/CPU机群实现方案研究

叠前逆时偏移是当前最为准确的地震成像方法,由于计算量大、存储量大等原因需要合适的实现策略和高效的计算平台.本文以高阶有限差分逆时偏移为基础,重点讨论了在GPU上实现需要解决的显存不足问题和人工边界问题.利用区域分解技术可以在当前GPU上高效地实现任意生产规模的三维逆时偏移成像,不会受到GPU显存规模的制约.常规最佳匹配层边界条件边界区域控制方程与内部区域差异较大,不适于GPU高速运算.本文在GPU上实现近似最佳匹配层(NPML)边界条件,使得高阶有限差分计算不需要分支判断,边界区域辅助波场的存储量也较低,保证了在GPU上进行波场传播的高效性.三维理论数据和实际资料成像结果表明了本文方法的正确性.     

热带海盆对热力强迫的线性响应

通过对线性两层海洋模式进行正交模求解,得到了热带矩形海盆在热力强迫下的海洋动力场水平结构.在这个线性两层模式中,没有施加风应力,仅考虑了热力强迫下的Rayleigh摩擦和Newton冷却效应.在一种理想化的经向不均匀加热强迫下,动力场表现出类似于风生环流的特征:窄而强的西边界区,宽而弱的东边界区;具有双涡(double-gyre)结构.线性响应中斜压模态比正压模态大一个量级,在响应中占主要地位.     

Rossby波的螺旋斑图

应用描写大气大尺度运动的准地转方程组，求得了大气Rossby波的三维定常流场以及相应的位温场、涡度场和散度场，其中的三维流场构成了物理空间的一个非线性自治动力系统. 研究表明，Rossby波具有     

Formation of the thermal-driven boundary jet in an f-plane mesoscale basin

The paper adopts an f-plane quasi-geostrophic inertial model without linearization to investigate the perturbation temperature, boundary jet and upwelling (downwelling) in an idealized rectangular basin, under the consideration of west side friction layer and heat conservation. There is net heat input on the upper surface and equal quality heat dissipation on the west boundary, and without heat exchange on other boundaries, then the heat is conservation in the whole basin. Results show that there is thermal front due to denseness of the perturbation temperature in the west side boundary, the perturbation pressure and flow field are reversal on the upper layer and bottom layer. On the bottom layer, the west coastal current is northward, and the maximum perturbation pressure center is on the west, however, on the upper layer, the east coastal current is southward, and the maximum perturbation pressure center is on the east. There is strong vertical flow in narrow western boundary layer, and also in the central zone. The effect of different upper thermal forcings is also studied, and it can be concluded that there is always temperature denseness and boundary jet near the west boundary, and the appearance of flow field reversal, but the distribution of vertical flow is rather different.     

The equatorial dynamics of a shallow,homogeneous ocean

Abstract

It is shown that the linear equatorial dynamics of a shallow ocean is characterized by two boundary layers of width γ^? L and γL (γ is the Ekman number of the flow, assumed small, and L is a horizontal dimension of the basin). In the γ^? layer stress in the bottom Ekman layer is comparable to that in the surface Ekman layer. In the γ layer vertical friction is important throughout the depth of the ocean. Should the Rossby number ? be so large as to invalidate a linear theory (? > γ^5/3), then inertial effects become important at a distance ?^2/5 L from the equator. The role played in the circulation of the basin by the non-linear equatorial current first studied by Charney (1960) is shown to be similar to that of the γ layer of the linear theory. Though lateral friction is unimportant in a linear model of the flow, shear layers at the equator are found to be a necessary feature of non-linear flow.     

Inertial effects in an oceanic circulation model

Abstract

The flow in a mechanically driven thin barotropic rotating fluid system is analysed. The linear theory of Baker and Robinson (1969) is modified and extended into the non-linear regime.

An internal parameter, the “local Rossby number”, is indicative of the onset of nonlinear effects. If this parameter is 0(1) then inertial effects are as important as Coriolis accelerations in the interior of the transport-turning western boundary layer and both of its Ekman layers. The inertial effects in the Ekman layers, ignored in previous explorations of non-linear wind driven oceanic circulation, are retained here and calculated using an approximation of the Oseen type. The circulation problem is reduced to a system of scalar equations in only two independent variables; the system is valid for non-small local Rossby number provided only that the approximate total vorticity is positive.

To complete the solution for small Rossby number a boundary condition for the inertially induced transport is needed. It is found by examining the dynamics controlling this additional transport from the western boundary layer as the transport recirculates through the rest of the ocean basin. The strong constraint of total recirculation within the western boundary layer (zero net inertial transport) is derived.

The calculated primary inertial effects are in agreement with the observations of the laboratory model of Baker and Robinson (1969).

The analysis indicates the extent to which three-dimensional non-linear circulation can be reduced to a two dimensional problem.     

The baroclinic circulation structure of Yellow Sea Cold Water Mass

The Yellow Sea is a semi-enclosed shallow sea with a deep trough of about 80 m. On the hy-drographic condition in the Yellow Sea, Lie[1] pointed out that it is strongly associated with winter cooling and summer heating, fresh input from rivers into the co…     

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.     

A model study of spin-down and circulation in a cold water dome

A three-dimensional prognostic hydrodynamic model in cross sectional form is used to examine the influence of bottom friction, mixing and topography upon the spin-down and steady-state circulation in a cold water bottom-dome. Parameters characteristic of the Irish Sea or Yellow Sea cold water domes are used. In all calculations, motion is induced by specifying an initial temperature distribution characteristic of the dome, and an associated along frontal flow. The spin-down of the dome is found to be influenced by the coefficient of bottom friction, with a typical time scale of order 10 days, and in general to be independent of the chosen initial vertical profile of along frontal flow. However, in the case in which the along frontal flow is such that the near bed velocity is zero, then bottom stress is also zero, and there is no appreciable spin-down. Calculations showed that the formulation of viscosity and diffusivity had a greater effect upon the steady-state circulation than topography, suggesting that background mixing of tidal origin is important. The lack of topographic influence was due mainly to the formulation of the initial conditions which were taken to be independent of topography. The steady-state circulation was characterized by a cyclonic flow in the surface region, with an anti-cyclonic current near the bed, where frictional effects produced a bottom Ekman layer and an across frontal flow. This gave rise to vertical circulation cells in the frontal region of the dome with prevailing downwelling motion inside the dome. A detailed analysis of the dynamic balance of the various terms in the hydrodynamic equations yielded insight into the processes controlling the steady-state circulation in cold water domes. Responsible Editor: Phil Dyke     

The bottom Ekman layer and the apparent violation of the maximum principle

The solution for the bottom Ekman layer has a somewhat counter intuitive character, which seems to violate the maximum principle: at a certain level the velocity within the Ekman layer is higher than the velocity in the geostrophic layer above. I explain this character by looking at an analogous problem in an inertial frame of reference and show that it is the result of observing the flow from a rotating frame of reference (i.e. within a system that is not in steady state). The flow in the bottom Ekman layer is a superposition of the flow that results from the force exerted on the fluid by the rotating Earth and of the flow that results from the pressure-gradient term. Therefore, at a certain level the speed is higher than the speed of the geostrophic layer above which results from the pressure gradient alone.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

A 3-D coastal tidal rectification process: observations, theory and experiments

In homogeneous rotating fluid, when there is an oscillating forcing in the interior fluid with a period long enough for an Ekman layer to develop, there is an interaction between the oscillatory Ekman layer and the vertical wall, since the latter imposes an alternating adjustment flow confined near the wall. As a result, this coastal rectification process leads to a Lagrangian transport along the coast. The Ekman number, the Rossby number and the temporal Rossby number of the forcing flow are the governing parameters of that mechanism which can be described by a simplified analytical model taking into account both the vertical time-dependent structure of the current and the presence of the wall. The model shows that the residual (rectified) current flowing with the coast to its right results from the strong nonlinear interaction between along- and cross-shore tidal currents leading to asymmetrical momentum exchanges between the Ekman bottom layer and the coastal boundary layer. The model provides simple scaling laws for the maximum intensity and width of the residual current. The latter is significantly larger than the friction (Stokes) lateral boundary layer of the forcing flow. A comprehensive set of experiments is performed in the 13 m diameter rotating tank by oscillating an 8 m×2 m horizontal plate and vertical wall in a homogeneous fluid at rest in solid-body rotation and measuring the two horizontal components of the current at several locations and depths above the central part of the plate. The predicted and experimentally measured maximum intensity and width of the residual current are in very good agreement, within the range of validity of the model, i.e. when the Ekman number is sufficiently small. However experiments also show that the residual current still occurs when the Ekman layer thickness is of the same order as the fluid depth, but it is then confined to a narrower band along the vertical wall. The flow structure found experimentally is also correctly described by a numerical model developed by Zhang et al. (1994). Current measurements in the Eastern part of the English Channel near the French coast reveal a significant coastal residual current flowing Northward and the coastal rectification process described here may account for part of it.     

A three-dimensional model study of near-inertial motion: generation and influence of an along-shelf flow

A three-dimensional baroclinic model of the Balearic Sea region is used to examine the processes influencing the distribution of near-inertial currents and waves in the region. Motion is induced by a spatially uniform wind impulse. By using a uniform wind, Ekman pumping due to spatial variability in the wind is removed with the associated generation of internal waves. However, internal waves can still be produced where stratification intersects topography. The generation and propagation of these waves, together with the spatial distribution of wind-forced inertial oscillations, are examined in detail. Diagnostic calculations show that in the near-coastal region inertial oscillations are inhibited by the coastal boundary. Away from this boundary the magnitude of the inertial oscillations increases, with currents showing a 180° phase shift in the vertical. The inclusion of an along-shelf flow modifies the inertial currents due to non-linear interaction between vorticity in the flow and the inertial oscillations. Prognostic calculations show that besides inertial oscillations internal waves are generated. In a linear model the addition of an along-shelf flow produces a slight reduction in the energy at the near-inertial frequency due to enhanced viscosity associated with the flow and changes in density field. The inclusion of non-linear effects modifies the currents due to inertial oscillations in a manner similar to that found in the diagnostic model. A change in the effective inertial frequency also influences the propagation of the internal waves. However, this does not appear to be the main reason for the enhanced damping of inertial energy, which is due to the along-shelf advection of water of a different density into a region and increased viscosity and mixing associated with the along-shelf flow.Responsible Editor: Phil Dyke