A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING

Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.

The Solitary Waves of the Barotropic Quasi-Geostrophic Model with the Large-scale Orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.

Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

Bcklund Transformations and Explicit Solutions of (2+1)-Dimensional Barotropic and Quasi-Geostrophic Potential Vorticity Equation

By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.

Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

Charney’s Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic;when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.

A THREE-DIMENSIONAL COASTAL BAROTROPIC MODEL IN GENERALIZED CURVILINEAR GRIDS

The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.

Numerical Physical Mechanism and Model of Turbulent Cascades in a Barotropic Atmosphere

In a barotropic atmosphere, new Reynolds mean momentum equations including turbulent viscosity, dispersion, and instability are used not only to derive the KdV-Burgers-Kuramoto equation but also to analyze the physical mechanism of the cascades of energy and enstrophy. It shows that it is the effects of dispersion and instability that result in the inverse cascade. Then based on the conservation laws of the energy and enstrophy, a cascade model is put forward and the processes of the cascades are described.

THE DIABATIC WAVES IN BAROTROPIC MODEL

The equations of barotropic model are used to discuss the effects of diabatic factors such as heat-ing of convective condensation, evaporation-wind feedback and CISK on the Rossby wave and the Kelvin wave. In low latitudes we have obtained the angular frequency and analyzed the period and stability of waves. The result shows the existence of the diabatic factors not only enlarges the period of adiabatic waves but also changes the stability of waves. Thus we think that the so-called intraseasonal oscillation and some other low-frequency oscillations are a kind of diabatic waves which are important factors producing the long-term weather changes and short-term climatic evolution.

Nondispersive Periodic Solution of a Barotropic Semi-Geostrophic Model

The existence and solution of the non-dispersive periodic solution are achieved concerning nonlinear barotropic Rossby waves of a barotropic semi-geostrophic model, demonstrating the likelihood of the Taylor evolution, together with the related dimensionless a-criterion. Finally, the wave velocity expression is proposed with some diagnostic relations among the wave parameters.

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model.The results suggest that compared with rays in the nondivergent barotropic model,rays in the divergent model can have enhanced meridional and zonal propagation,accompanied by a more dramatic variability in both wave energy and amplitude,which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model.For rays propagating in a region enclosed by a turning latitude and a critical latitude,the wave energy approaches the maximum value inside the region,while the amplitude approaches the maximum at the turning latitude.Waves can develop when both the wave energy and amplitude increase.For rays propagating in a region enclosed by two turning latitudes,the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude,while the total wavenumber approaches the maximum value inside the region.The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly.The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy,which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.

A Simple Quasi-Geostrophic Coupled Ocean-Atmosphere Model

The quasi-geostrophic atmospheric and oceanic equations of momentum and thermodynamics with dissipation factors are used to create a simple coupled ocean-atmosphere model describing the large-scale shallow-water motion. We discuss the ocean-atmosphere coupling effect in mid-high and low latitudes separately and analyze characteristics of which the oscillatory periods of coupled low-frequency modes (ocean mode) vary with the coupling frequency and latitudinal number. This can interpret the correlation between low-frequency oscillation and ocean-atmosphere interaction. Then from the dispersion curves of atmosphere and ocean, we reveal effect of the coupling strength on the propagation of Rossby waves. The convection mechanism between the two modes is also discussed in view of the slowly varying wave train.The results show that Newtonian cooling and Rayleigh friction play a stable rule in oceanic Rossby waves, the period of coupled low-frequency mode grows with the increment of the coupling frequency. The larger the latitudinal number is, the more rapidly it grows. When the coupling frequency tends to critical value, the oceanic Rossby waves become static. When the ocean-atmosphere coupling strength grows to some degree, the propagation of oceanic Rossby waves will become opposite to its original direction. One part of the oceanic Rossby waves is converted into atmospheric Rossby waves, the energy conversion coefficient is also solved out.

Analysis-Prediction Experiments over Indian Region Using Primitive Equation Barotropic Model

The impact of initial guess and grid resolutions on the analysis and prediction has been investigated over the Indian region. For this purpose, an univariate objective analysis scheme and a primitive equation barotropic model have been used. The impact of initial guess and the resolutions on analysis and prediction is discussed.

Comparison of Flow Characteristics Around Refractive and Right-angled Groins in Barotropic and Baroclinic Conditions

Groins are employed to prevent nearshore areas from erosion and to control the direction of flow. However, the groin structure and its associated flow characteristics are the main causes of local erosion. In this study, we investigate the flow patterns around refractive and right-angle groins. In particular, we analytically compare the flow characteristics around a refractive groin and study the degree of accuracy that can be achieved by using a right-angle groin of various projected lengths. To compare the flow characteristics, we replaced the right-angle groin with an approximation of a refractive groin. This replacement had the least effect on the maximum velocity of flow in the channel. Moreover, we investigated the distribution of the density variables of temperature and salinity, and their effects on the flow characteristics around the right-angle groin. A comparison of the flow analysis results in baroclinic and barotropic conditions reveals that the flow characteristic values are very similar for both the refractive and right-angle groins. The geometry of the groin, i.e., right-angle or refractive, has little effect on the maximum speed to relative average speed. Apart from the angular separation, the arm length of the groin in downstream refractive groins has less effect on other flow characteristics than do upstream refractive groins. We also correlated a number of non-dimensional variables with respect to various flow characteristics and groin geometry. These comparisons indicate that the correlation between the thalweg height and width of the channel and groin arm＇s length to projection length have been approximated using linear and nonlinear formulas regardless of inner velocity in the subcritical flow.

耦合模式FGOALS-g3对全球海洋潮汐的模拟评估

潮汐在海洋能量的传递和混合过程中起着重要的作用,为维持全球热盐环流提供了主要的能量,影响着全球的海洋环流。此前已有工作在低分辨率的、单独的海洋模式中研究潮汐作用对海洋环流状态的敏感性,为进一步研究潮汐作用对环流和气候状态的敏感性,有必要将潮强迫引入到气候耦合模式中。本文成功地将8个主要平衡分潮显式地加入到耦合模式FGOALS-g3中,并评估了其对全球海洋潮汐的模拟能力,对于进一步研究潮汐对大尺度环流及气候状态的影响有重要意义。本文通过对模拟的海表面高度数据进行潮汐调和分析,得到各个分潮的调和常数,并将其与全球潮汐模型TPXO9和FES2014,以及开放海洋潮汐数据集st102进行对比。结果表明,FGOALS-g3耦合模式可以合理地模拟全球海洋中的正压潮,模拟结果与潮汐模型和实测数据集相比均比较接近。与这两套全球潮汐模型相比,均方误差均相对较小,且误差大多分布在振幅较大的区域。与st102数据集相比,FGOALS-g3模拟的8个主要分潮的平均振幅相对误差均在10%以内,且总均方误差均小于10 cm。

基于POM的全球M_(2)正压潮数值模拟

普林斯顿海洋模型(POM)是应用较为广泛的区域海洋数值模型,但在全球潮汐数值模拟中的适用性尚待检验。本研究将三极网格和潮汐势引入POM中,对包含北极点的海洋潮波问题进行模拟,并建立水平分辨率1°×1°的全球大洋潮波数值模型,对全球M_(2)正压潮波进行数值模拟。模拟结果显示,太平洋存在5个M_(2)分潮无潮点,大西洋存在4个M_(2)分潮无潮点,印度洋存在3个M_(2)分潮无潮点,北冰洋存在2个M_(2)分潮无潮点;总体来看,大洋M_(2)分潮振幅小于近岸振幅,赤道太平洋海域出现2个M_(2)分潮的高振幅区,北冰洋与其他三大洋相比振幅最小。POM模拟结果与TPXO7.2全球潮汐同化模型结果基本一致,两者振幅均方根误差为5.6 cm,迟角均方根误差为10.0°,振幅的平均相对误差为12.5%;POM模拟结果与全球潮汐常数(GTCs)数据集对比,两者振幅均方根误差为21.4 cm,迟角的均方根误差为29.1°,振幅的平均相对误差为25.1%。表明所构建的POM全球大洋潮波模型能够较为准确地模拟全球潮波,得到全球潮汐的分布特征,为POM应用于其他全球海洋动力过程研究提供借鉴和参考。

A class of asymptotic solution for the time delay wind field model of an ocean

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.

An interacting two-fluid scenario for dark energy in a Bianchi type-I cosmological model

We study the evolution of the dark energy parameter within a Bianchi type-I cosmological model filled with barotropic fluid and dark energy. The solutions have been obtained for power law and exponential forms of the expansion parameter （they correspond to a constant deceleration parameter in general relativity）. After a long time, the models tend to be isotropic under certain conditions.

A LATTICE BOLTZMANN MODELING FOR THE WESTERN BOUNDARY CURRENT IN A LINEAR WIND-DRIVEN QUASI-GEOSTROPHIC MODEL

The linear barotropic vorticity equation describing wind-driven oceancirculation is considered as a convection-diffusion equation that can be numerically solved bylattice Boltzmann method. Numerical experiments are carried out to examine the validity of the modelfor the wind-driven circulation. When horizontal viscosity is constant and spatially uniform, allnumerical solutions for different parameters approach analytical solutions well. The spatiallyvarying horizontal viscosity is also included in this model. It is shown that the variant horizontalviscosity increases the meridional transport significantly in west boundary current. By theinvestigation of numerical results, it was concluded that this model is competent for simulatingwestern boundary current.

基于解析四维集合变分的全球正压谱模式初始场优化研究

解析四维集合变分数据同化方法是一种无需伴随的、完全继承四维变分非线性处理能力的、“流依赖”的非顺序数据同化方法。本研究基于解析四维集合变分,开展全球正压谱模式初始场优化研究,验证解析四维集合变分的同化能力,并构建了高效的扰动集合成员生成方案,将解析四维集合变分降维到了样本空间,最后检验了解析四维集合变分对同化积分窗口长度和观测采样间隔的敏感性。试验结果表明,解析四维集合变分能优化全球正压谱模式的初始场,降维到样本空间后,只需要80个集合成员就可以取得很好的同化效果,在较长的同化积分窗口和观测采样间隔的条件下也可以达到理想的同化效果。