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1.
《Ocean Modelling》2010,31(4):310-322
A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.  相似文献   

2.
A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.  相似文献   

3.
An attempt is made to examine some observational and theoretical aspects of upper ocean dynamics in regions of strong coastal upwelling. “Upper ocean” is roughly defined as about the upper 10–30 m of the water column for most systems. First, the basic surface Ekman and mixed layers are discussed, including some of the modifications due to upwelling. Next, coastal upwelling fronts and their associated circulation are treated. Finally, areas of strongly three-dimensional upwelling are classified and discussed. Horizontal advection of heat and momentum appear to be generally important for the near-surface dynamics of coastal upwelling, and these phenomena make realistic theoretical treatments especially difficult.  相似文献   

4.
引潮力对海洋环流模式的影响   总被引:2,自引:1,他引:1  
The eight main tidal constituents have been implemented in the global ocean general circulation model with approximate 1° horizontal resolution.Compared with the observation data,the patterns of the tidal amplitudes and phases had been simulated fairly well.The responses of mean circulation,temperature and salinity are further investigated in the global sense.When implementing the tidal forcing,wind-driven circulations are reduced,especially those in coastal regions.It is also found that the upper cell transport of the Atlantic meridional overturning circulation(AMOC) reduces significantly,while its deep cell transport is slightly enhanced from 9×106m3/s to 10×106 m3/s.The changes of circulations are all related to the increase of a bottom friction and a vertical viscosity due to the tidal forcing.The temperature and salinity of the model are also significantly affected by the tidal forcing through the enhanced bottom friction,mixing and the changes in mean circulation.The largest changes occur in the coastal regions,where the water is cooled and freshened.In the open ocean,the changes are divided into three layers:cooled and freshened on the surface and below 3 000 m,and warmed and salted in the middle in the open ocean.In the upper two layers,the changes are mainly caused by the enhanced mixing,as warm and salty water sinks and cold and fresh water rises;whereas in the deep layer,the enhancement of the deep overturning circulation accounts for the cold and fresh changes in the deep ocean.  相似文献   

5.
A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed.  相似文献   

6.
The fidelity of numerical simulations of the general circulation of the North Atlantic Ocean in basin- to global-scale models have improved considerably in the last several years. This improvement appears to represent a regime shift in the dynamics of the simulated flow as the horizontal grid spacing decreases to around 10 km. Nevertheless, some significant biases in the simulated circulation and substantial uncertainties about the robustness of these results with respect to parameterization choices remain. A growing collection of simulations obtained with the POP primitive equation model allow us to investigate the convergence properties and sensitivity of high resolution numerical simulations of the North Atlantic, with particular attention given to Gulf Stream separation and the subsequent path of the North Atlantic Current into the Northwest Corner. Increases in resolution and reductions in dissipation both contribute to the improvements in the circulation seen in recent studies. We find that our highest resolution eddy-resolving simulations retain an appreciable sensitivity to the closure scheme. Our most realistic simulations of the Gulf Stream are not obtained at the lowest levels of dissipation, while the simulation of the North Atlantic Current continues to improve as dissipation is reduced to near the numerical stability limit. In consequence, there is a limited range of parameter space where both aspects of the simulated circulation can be brought into agreement with observations. This experience gained with the comparatively affordable regional North Atlantic model is now being used to configure the next generation of ocean climate models.  相似文献   

7.
Simulations from a coupled ice–ocean model that highlight the importance of synoptic forcing on sea-ice dynamics are described. The ocean model is a non-hydrostatic primitive equation model coupled to a dynamic thermodynamic sea ice model. The ice modelling sensitivity study presented here is part of an ongoing research programme to define the role played by sea ice in the energy balance of the Greenland Sea. The different categories of sea ice found in the subpolar regions are simulated through the use of equations for thin ice, thick ice and the Marginal Ice Zone. A basin scale numerical model of the Greenland, Iceland and Norwegian Seas has a horizontal resolution of 20 km and a vertical grid spacing of 50 m. This resolution is adequate for resolving the mesoscale topographic structures known to control the circulation in this region. The spin-up reproduces the main features of the circulation, including the cyclonic gyres in the Norwegian and Greenland Basins and Iceland Plateau. Topographic steering of the flow is evident. The baroclinic Rossby radius of deformation is between 5 and 10 km so that the model is not eddy-resolving. The coupled ice–ocean model was run for a period of two weeks. The influence of horizontal resolution of the atmospheric model was tested by comparing simulations using six hourly wind fields from the ECMWF with those generated using six hourly fields from a HIRLAM, with horizontal resolutions of 1° and 0.18° respectively. The simulations show reasonable agreement with satellite ice compactness data and data of ice transports across sections at 79°N, 75°N and Denmark Strait.  相似文献   

8.
Within the European DIADEM project, a data assimilation system for coupled ocean circulation and marine ecosystem models has been implemented for the North Atlantic and the Nordic Seas. One objective of this project is to demonstrate the relevance of sophisticated methods to assimilate satellite data such as altimetry, surface temperature and ocean color, into realistic ocean models. In this paper, the singular evolutive extended Kalman (SEEK) filter, which is an advanced assimilation scheme where three-dimensional, multivariate error statistics are taken into account, is used to assimilate ocean color data into the biological component of the coupled system. The marine ecosystem model, derived from the FDM model [J. Mar. Res. 48 (1990) 591], includes 11 nitrogen and carbon compartments and describes the synthesis of organic matter in the euphotic zone, its consumption by animals of upper trophic levels, and the recycling of detritic material in the deep ocean. The circulation model coupled to the ecosystem is the Miami isopycnic coordinate ocean model (MICOM), which covers the Atlantic and the Arctic Oceans with an enhanced resolution in the North Atlantic basin. The model is forced with realistic ECMWF ocean/atmosphere fluxes, which permits to resolve the seasonal variability of the circulation and mixed layer properties. In the twin assimimation experiments reported here, the predictions of the coupled model are corrected every 10 days using pseudo-measurements of surface phytoplankton as a substitute to chlorophyll concentrations measured from space. The diagnostics of these experiments indicate that the assimilation is feasible with a reduced-order Kalman filter of small rank (of order 10) as long as a sufficiently good identification of the error structure is available. In addition, the control of non-observed quantities such as zooplankton and nitrate concentrations is made possible, owing to the multivariate nature of the analysis scheme. However, a too severe truncation of the error sub-space downgrades the propagation of surface information below the mixed layer. The reduction of the actual state vector to the surface layers is therefore investigated to improve the estimation process in the perspective of sea-viewing wide field-of-view sensor (SeaWiFS) data assimilation experiments.  相似文献   

9.
The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping.A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton’s method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored.  相似文献   

10.
We present two calculations of pollutant dispersal in the Pacific Ocean: (1) during possible ship-wrecks in the process of spent nuclear fuel transportation from Petropavlovsk-Kamchatsky and (2) pollutant spread from the Japanese coast after the Fukushima-1 nuclear disaster on March 11, 2011. The circulation was calculated using a σ model of ocean hydrothermodynamics developed at the Institute of Numerical Mathematics (INM), Russian Academy of Sciences (RAS); it is adapted to cover the Pacific Ocean basin from the equator to the Bering Strait with a high (1/8)° spatial resolution and it is capable of reproducing the mesoscale ocean variations. The pollutant dispersal in the case of possible shipwrecks was estimated for currents characteristic for a statistically average year with atmospheric forcing in accordance with the so-called normal CORE year data. The pollution spread from the Fukushima-1 nuclear power plant (NPP) was estimated by calculating the circulation with the real atmospheric forcing in accordance with the NCEP analysis data obtained from the Hydrometeorological Centre of Russia. It is noteworthy that a simplified assimilation of the observed sea surface temperature (SST) was performed. In both cases the currents were calculated simultaneously with the transport calculation of the pollutant as a passive admixture, which corresponds to a real-time calculation of pollutant transport. A map analysis of pollution dispersal shows that the horizontal transport is substantially more intense in the upper ocean layers than in deep ones. Therefore, like in the North branch of Kuroshio, pollutants can be delivered to the deep layers not through deep-water horizontal transport, but rather as a result of vertical downwelling from the already contaminated upper layers. However, the complex three-dimensional structure of the horizontal and vertical transport may lead to reverse situations. A calculation of pollution transport from the Fukushima-1 NPP showed that radioactive pollution would propagate eastward and not present the danger for Russian territory. Moreover, even for an exaggerated scenario of pollution emission, the background pollution level will be exceeded only in a narrow region within 50 km of the Japanese coast.  相似文献   

11.
We consider the possibility of assimilating sea surface temperature data by a combined ocean dynamics model incorporating a three-dimensional hydrodynamic model for synoptic variability for the considered ocean area and an integral model block describing the upper mixed layer. Model numerical simulations and experiments involving satellite-derived data are analysed.Translated by V. Puchkin.  相似文献   

12.
A new three-dimensional numerical model is derived through a wave average on the primitive N-S equations, in which both the"Coriolis-Stokes forcing" and the"Stokes-Vortex force" are considered. Three ideal experiments are run using the new model applied to the Princeton ocean model (POM). Numerical results show that surface waves play an important role on the mixing of the upper ocean. The mixed layer is enhanced when wave effect is considered in conjunction with small Langmuir numbers. Both surface wave breaking and Stokes production can strengthen the turbulent mixing near the surface. However, the influence of wave breaking is limited to a thin layer, but Stokes drift can affect the whole mixed layer. Furthermore, the vertical mixing coefficients clearly rise in the mixed layer, and the upper ocean mixed layer is deepened especially in the Antarctic Circumpolar Current when the model is applied to global simulations. It indicates that the surface gravity waves are indispensable in enhancing the mixing in the upper ocean, and should be accounted for in ocean general circulation models.  相似文献   

13.
A new version of the Institute of Atmospheric Physics, Russian Academy of Sciences (IAP RAS), climate model (CM) has been developed using an ocean general circulation model instead of the statistical-dynamical ocean model applied in the previous version. The spatial resolution of the new ocean model is 3° in latitude and 5° in longitude, with 25 unevenly spaced vertical levels. In the previous version of the oceanic model, as in the atmospheric model, the horizontal resolution was 4.5° in latitude and 6° in longitude, with four vertical levels (the upper quasi-homogeneous layer, seasonal thermocline, abyssal ocean, and bottom friction layer). There is no correction for the heat and momentum fluxes between the atmosphere and ocean in the new version of the IAP RAS CM. Numerical experiments with the IAP RAS CM have been performed under current initial and boundary conditions, as well as with an increasing concentration of atmospheric carbon dioxide. The main simulated atmospheric and oceanic fields agree quite well with observational data. The new version’s equilibrium temperature sensitivity to atmospheric CO2 doubling was found to be 2.9 K. This value lies in the mid-range of estimates (2–4.5 K) obtained from simulations with state-of-the-art models of different complexities.  相似文献   

14.
Intercomparison of three South China Sea circulation models   总被引:2,自引:1,他引:1  
1IntroductionTheSouthChinaSeaisthelargesttropicalmarginaldeepsealocatingbetweenthewesternPacificOceanandtheeasternIndianOcean.AsapartofAsia-Australiamaritimecontinent,monsoonisaprimaryfactorforcingtheSouthChinaSeaCurrent(SCSC)variation.Drivenbynortheasterlymonsooninwinterandsouth-westerlymonsooninsummer,respectively,theSCSCbehavesacyclonicgyreandananticy-clonicgyre,correspondingly(Wyrtki,1961;Xuetal.,1982).Owingtotheshortageandexpen-sivenessofdirectobservationsintheSCS,fur-therunder…  相似文献   

15.
The southwestern tropical Atlantic (05°S–25°S/20°W–47°W), where part of the South Equatorial Current (SEC) enters at its eastern border, is of particular interest as it is fed by many western boundary currents along the eastern Brazilian continental shelf. However, the long-term variability of the dynamics in this region, which are also important as they contribute to the climate over northeastern Brazil, is largely unknown. We use the Regional Ocean Model System (ROMS) here for the first time in this area to simulate the ocean circulation with an isotropic horizontal grid resolution of 1/12° and 40 terrain-following layers. As a primary evaluation of the ROMS configuration, we explore surface and vertical thermal structures, the surface mixed layer, and mass transports within the upper levels. Interannual variability results are compared with the first two-year series of observed thermal profiles derived from the three PIRATA-SWE moorings. The simulated thermal structure in the upper ocean layers agrees well with in-situ data. ROMS simulations point out a broad and relatively weak SEC flow composed of a sequence of more or less defined near-surface cores. The westward SEC transport for the upper 400 m along the PIRATA-SWE section, calculated from the ROMS simulation for 2005–2007, shows an average volume transport of 14.9 Sv, with a maximum observed in JFM (15.7 Sv), and a minimum during MJJ (13.8 Sv). ROMS results indicate that the 2005–2007 seasonal near-surface westward SEC transport is modulated by the zonal wind variability. Three zonal sections extending from the American continent to the PIRATA buoy sites confirm that stronger northward NBUC transport and decreasing BC transport were achieved during May 2006 and May 2007, i.e. at the time the sSEC bifurcation reaches its southernmost position. On the other hand, the maximum southward BC flow was verified during January 2006, January 2007 and March 2007, with a minimum northward NBUC flow in December 2005 and October/December 2006, corresponding to the period when the sSEC bifurcation reaches its lowest latitude (OND). Sea Surface Height (SSH) and the surface Eddy Kinetic Energy (EKE) derived from simulations and AVISO Rio05 product point out the highest surface meso-scale activity (EKE  50 cm2 s−2) along the cSEC and NBUC/BC patches. Preliminary results provide additional ingredients in the complexity of the SEC divergence region and encourage us to conduct a more detailed exploration of the dynamics of this region using the ROMS. This also shows the need to continue, extend, and vertically upgrade the observational PIRATA-SWE array system, especially with more levels of salinity measurements and the installation of current measurements.  相似文献   

16.
Horizontal and meridional volume transports on timescales from intra-seasonal to interannual in the North Pacific subarctic region were investigated using a reanalysis dataset for 1993–2001 that was constructed from an assimilation of the TOPEX altimeter and in situ data into an eddy-permitting North Pacific ocean general circulation model. The barotropic flow is excited along east of the Emperor Seamounts by the western intensification dynamics. The volume transport of this flow compensates for that across the interior region east of the Seamounts below the summit depth of the Seamounts. The Oyashio, which is also considered as a compensation flow for the transport in the whole interior region, includes baroclinic as well as barotropic components. Baroclinic transports in the whole interior region exceed those in the western boundary region in the upper (200–1000 m) and lower (2000–5000 m) layers, and the total transport is northward (southward) in the upper (lower) layer. These excesses of the baroclinic transport are balanced by a vertical transport of the meridional overturn. The meridional overturn has a complementary relation to the basin-scale baroclinic circulation in the North Pacific subactic region. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

17.
2011年3月日本福岛核电站核泄漏在海洋中的传输   总被引:2,自引:0,他引:2  
使用全球版本的迈阿密等密度海洋环流模式对2011年3月日本福岛核电站泄漏在海洋中的传输以及扩散进行了数值模拟。数值模式中核废料(示踪物)排放情景采取等通量连续排放,排放时间从3月25日开始,分别持续20 d以及1 a,两种情形分别积分20 a。为了减少海洋环流年际变化带来的数值模拟的的不确定性,20 a的模式积分分别用2010年、1991-2011年、1971-1991年以及1951-1971年4个不同时段的NCEP/NCAR逐日再分析资料作为大气强迫场,因此每种排放情形包含4个数值试验。模拟结果的分析表明,不同核废料排放情景及其在不同时段大气资料对海洋模式的驱动下,模拟的示踪物总体的传输扩散路径(包括表层以及次表层)、传输速率以及垂直扩展的范围没有显著的差异。集合平均数值模拟的结果显示:在两种排放情景下,日本福岛核泄漏在海洋的传输路径受北太平洋副热带涡旋洋流系统主导,其传输路径首先主要向东,到达东太平洋后,再向南向西扩散至西太平洋,可能在10~15 a左右影响到我国东部沿海海域,且海洋次表层的传输信号比表层信号早5 a左右。通过进一步分析模式积分过程中最大示踪物浓度随时间变化发现,在积分第20 a(2031年3月),海洋表层和次表层浓度的最高值分别只有模式积分第一年浓度的0.1%和1%。在积分的20 a里,排放的核废料主要滞留在北太平洋海域(超过86%±1.5%的核废料在积分结束时,滞留在北太平洋),而在积分的前10 a(2021年之前),几乎所有的核废料滞留在北太平洋;在核废料的垂直分布上,主要集中在海洋表层至600 m的深度,在积分的20 a时间里,没有核废料信号扩散至1 000 m以下的深度。数值模拟的结果也表明核废料浓度减弱的强度以及演变的时间特征主要受洋流系统的影响,与排放源的排放时间长短关系不大。值得指出的是,更加准确地评估一个真实的核泄漏事故对海洋环境所造成的可能影响,还需要考虑大气中的放射性物质的沉降以及海洋生态对核物质的响应。  相似文献   

18.
使用全球版本的迈阿密等密度海洋环流模式对2011年3月日本福岛核电站泄漏在海洋中的传输以及扩散进行了数值模拟。数值模式中核废料(示踪物)排放情景采取等通量连续排放,排放时间从3月25日开始,分别持续20 d以及1 a,两种情形分别积分20 a。为了减少海洋环流年际变化带来的数值模拟的的不确定性,20 a的模式积分分别用2010年、1991-2011年、1971-1991年以及1951-1971年4个不同时段的NCEP/NCAR逐日再分析资料作为大气强迫场,因此每种排放情形包含4个数值试验。模拟结果的分析表明,不同核废料排放情景及其在不同时段大气资料对海洋模式的驱动下,模拟的示踪物总体的传输扩散路径(包括表层以及次表层)、传输速率以及垂直扩展的范围没有显著的差异。集合平均数值模拟的结果显示:在两种排放情景下,日本福岛核泄漏在海洋的传输路径受北太平洋副热带涡旋洋流系统主导,其传输路径首先主要向东,到达东太平洋后,再向南向西扩散至西太平洋,可能在10~15 a左右影响到我国东部沿海海域,且海洋次表层的传输信号比表层信号早5 a左右。通过进一步分析模式积分过程中最大示踪物浓度随时间变化发现,在积分第20 a(2031年3月),海洋表层和次表层浓度的最高值分别只有模式积分第一年浓度的0.1%和1%。在积分的20 a里,排放的核废料主要滞留在北太平洋海域(超过86%±1.5%的核废料在积分结束时,滞留在北太平洋),而在积分的前10 a(2021年之前),几乎所有的核废料滞留在北太平洋;在核废料的垂直分布上,主要集中在海洋表层至600 m的深度,在积分的20 a时间里,没有核废料信号扩散至1 000 m以下的深度。数值模拟的结果也表明核废料浓度减弱的强度以及演变的时间特征主要受洋流系统的影响,与排放源的排放时间长短关系不大。值得指出的是,更加准确地评估一个真实的核泄漏事故对海洋环境所造成的可能影响,还需要考虑大气中的放射性物质的沉降以及海洋生态对核物质的响应。  相似文献   

19.
海洋环流是海洋系统物质能量收支、配置、平衡、维持和变化的关键通道与机制。从全球海洋视角,基于目前海洋环流多变率动力过程与趋势演变的认知,重点综述气候变化下海洋环流的海盆尺度三维联动特征机制、洋际交换与协同、世界大洋经向输运变化以及相关的海洋气候与环境生态效应,依据研究现状和需求,提出研究建议。结果表明:全球一致性变暖路径与进程调控下,受驱动因子的演变与胁迫,海洋环流变化对副热带中高纬地区年际、年代际气候与环境变迁具有突出作用影响,并可产生显著环境生态效应和严重致灾风险。建议加大专精特新观测仪器自主研发,通过国际合作加大中高纬海洋环流多尺度动力过程综合调查的参与度和主导性,增强多学科融合交叉研究力度,有效提升深层次海洋环流变异及动力、环境、生态灾害影响的气候变化综合风险预测预评估和防治能力,为海洋领域能源开发、生态系统保护、气候变化应对与灾害风险治理提供必要的动力学参考。  相似文献   

20.
A new high-resolution Eulerian numerical method is proposed for modelling quasigeostrophic ocean dynamics in eddying regimes. The method is based on a novel, second-order non-dissipative and low-dispersive conservative advection scheme called CABARET. The properties of the new method are compared with those of several high-resolution Eulerian methods for linear advection and gas dynamics. Then, the CABARET method is applied to the classical model of the double-gyre ocean circulation and its performance is contrasted against that of the common vorticity-preserving Arakawa method. In turbulent regimes, the new method permits credible numerical simulations on much coarser computational grids.  相似文献   

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