Approximate solution for mechanism of thermally and wind-driven ocean circulation

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method,...     

Singularly perturbed solution of coupled model in atmosphere-ocean for global climate

A box model of the interhemispheric thermohaline circulation （THC） in atmosphere-ocean for global climate is considered. By using the multi-scales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Secondly, by using the multi-scales, the first order approximate equation of the model is found. Finally, second order approximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multi-scales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.     

Adomian分解法在完全非线性S-G方程中的运用

为分析具有高非线性强度下的偏微分方程的初值问题,简化变量分离等方法带来的繁杂计算,研究了一类完全非线性Sine-Gordon方程以及它的近似方程(在|up|很小的情况下),经过适当的函数变换,运用改进的Ado-mian分解法解决了一些特殊情况下它们的初值问题,结合Talyor级数展开式,得到了一些精确解:扭结解(kink)、紧孤子解(compacton)、多重紧孤子解、compacton-kink解.另外运用线性化的方法结合不同形式的解得到它们一些更加丰富的新形式的精确解.     

Perturbed solving method for interdecadal sea-air oscillator model

A coupled system of the interdecadal sea-air oscillator model is studied.The El Nio-southern oscillation(ENSO) atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions.The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat-terns.This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory.The aim is to create an asymptotic solving method for the ENSO model.Employing the perturbed method,the asymptotic solution of corresponding problem is obtained,and the asymptotic behaviour of the solution is studied.Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.     

Tropical pacific decadal variability in subsurface temperature

The nature decadal variability of the equatorial Pacific subsurface temperature is examined in the control simulation with the Geophysical Fluid Dynamics Laboratory coupled model CM2.1.The dominant mode of the subsurface temperature variations in the equator Pacific features a 20-40 year period and is North-South asymmetric about the equator.Decadal variations of the thermocline are most pronounced in the southwest of the Tropical Pacific.Decadal variation of the north-south asymmetric Sea Surface wind in the tropical Pacific,especially in the South Pacific Convergence,is the dominant mechanism of the nature decadal variation of the subsurface temperature in the equatorial Pacific.     

Distribution of the tropical Pacific surface zonal wind anomaly and its relation with two types of El Niño

El Nio events with an eastern Pacific pattern(EP) and central Pacific pattern(CP) were first separated using rotated empirical orthogonal functions(REOF).Lead/lag regression and rotated singular value decomposition(RSVD) analyses were then carried out to study the relation between the surface zonal wind(SZW) anomalies and sea surface temperature(SST) anomalies in the tropical Pacific.A possible physical process for the CP El Ni o was proposed.For the EP El Ni o,strong westerly anomalies that spread eastward continuously produce an anomalous ocean zonal convergence zone(ZCZ) centered on about 165°W.This SZW anomaly pattern favors poleward and eastward Sverdrup transport at the equator.For the CP El Nio,westerly anomalies and the ZCZ are mainly confined to the western Pacific,and easterly anomalies blow in the eastern Pacific.This SZW anomaly pattern restrains poleward and eastward Sverdrup transport at the equator;however,there is an eastward Sverdrup transport at about 5°N,which favors the warming of the north-eastern tropical Pacific.It is found that the slowness of eastward propagation of subsurface warm water(partly from the downwelling caused by Ekman convergence and the ZCZ) is due to the slowdown of the undercurrent in the central basin,and vertical advection in the central Pacific may be important in the formation and disappearance of the CP El Nio.     

Dissipative travelling wave solution for El Niño tropic sea-air coupled oscillator

El Niño and Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.     

Preliminary study on the formation mechanism of counter western boundary undercurrents below the thermocline—A conceptual model

Based on a simple conceptual model of stratified ocean, the criterion of the geostrophic velocity inversion in and below the thermocline was derived ash′·ν′<0 and {ie1-1}, meaning that the slopes of the thermocline (h′) and the sea {ie1-2} must be opposite to each other, and thath′ must be strong enough to satisfy the latter inequality. The criterion was applied to discuss the features of the western boundary undercurrents, the counter undercurrents of the western boundary currents below the thermocline, and to discuss the dynamics of their formation finally resulting from the combination of the basin-scale circulation and local geostrophic balance. The formation mechanism, multicore structure, and transport variations of the Mindanao Undercurrent and those of other undercurrents, such as the North Equatorial Undercurrent and the Kuroshio undercurrent, can be satisfactorily explained by the above results. Research supported by the Postdoctoral Research Foundation and the NSFC (No. 49176255 and 49706066). Contribution No. 3405 from the Institute of Oceanology, Chinese Academy of Sciences.     

Wind-forced equatorial wave dynamics of the Pacific Ocean during 2014/2015 and 2015/2016 E1 Ni?o events

The equatorial wave dynamics of interannual sea level variations between 2014/2015 and2015/2016 El Nino events are compared using the Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics Climate Ocean Model(LICOM) forced by the National Centers for Environmental Prediction(NCEP) reanalysis I wind stre s s and heat flux during 2000-2015.In addition,the LICOM can reproduce the interannual variability of sea surface temperature anomalies(SSTA) and sea level anomalies(SLA) along the equator over the Pacific Ocean in comparison with the Hadley center and altimetric data well.We extracted the equatorial wave coefficients of LICOM simulation to get the contribution to SLA by multiplying the meridional wave structure.During 2014/2015 El Nino event,upwelling equatorial Kelvin waves from the western boundary in April2014 reach the eastern Pacific Ocean,which weakened SLA in the eastern Pacific Ocean.However,no upwelling equatorial Kelvin waves from the western boundary of the Pacific Ocean could reach the eastern boundary during the 2015/2016 El Nino event.Linear wave model results also demonstrate that upwelling equatorial Kelvin waves in both 2014/2015 and 2015/2016 from the western boundary can reach the eastern boundary.However,the contribution from stronger westerly anomalies forced downwelling equatorial Kelvin waves overwhelmed that from the upwelling equatorial Kelvin waves from the western boundary in 2015.Therefore,the western boundary reflection and weak westerly wind burst inhibited the growth of the 2014/2015 El Nino event.The disclosed equatorial wave dynamics are important to the simulation and prediction of ENSO events in future studies.     

Inversion calculation of the western Pacific boundary current during October, 1988

The inverse method developed by Wunsch (1978) is widely used to determine circulation in the oceans (Fu, 1980; Wunsch, Hu and Grant, 1983; Joyce and Wunsch, 1986; Rintoul, 1988). However, for inversion manipulation, measurements down to the bottom are required, and so is a certain solid boundary. In the present paper an equation of potential condition satisfied by the velocity field at the reference level is added to Wunsch's underdetermined matrix equation in order to make the method adequate for the case where measurements do not touch bottom and when a solid boundary does not exist. The western boundary current in the Pacific is calculated and examined in terms of the velocity field and transport with CTD data gathered by theR/V Science I in October 1988. Contribution No. 1748 from the Institute of Oceanology, Academia Sinica     

Approximate optimal tracking control for near-surface AUVs with wave disturbances

This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV’s system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.     

Interannual Variability of the Hadley Circulation Associated with Tropical Pacific SST Anomaly

The seasonal and interannual variability of zonal mean Hadley circulation are analyzed, and the important effects of sea surface temperature(SST), especially the tropical Pacific SST, on the meridional circulation are discussed. Following results are obtained: 1) the Hadley circulation presents a single clockwise(anticlockwise) cross-equator circulation in the Northern(Southern) Hemisphere winter,while it is a double-ring-shaped circulation quasi-symmetric about the equator in spring and autumn. The annual mean state just indicates the residual of the Hadley cell in winter and summer. 2) The first mode of interannual anomalies shows a single cell crossing the equator like the climatology in winter and summer but with narrower width. The second mode shows a double ring-shaped cell quasi-symmetric about the equator which is similar to the Hadley cell in spring or autumn. 3) Vertical motion of the Hadley circulation is driven by sea surface temperature(SST) through latent and sensible heat in the tropics, and the interannual anomalies are mainly driven by the SST anomaly(SSTa) in the tropical Pacific. 4) The meridional gradient of SSTa is well consistent with the lower meridional wind of Hadley circulation in the interannual part. For the spatial distribution, the meridional gradient of SSTa in the Pacific plays a major role for the first two modes while the effects of the Indian Ocean and the Atlantic Ocean can be ignored.     

非线性四阶边值问题的正解

利用锥不动点指数研究一类四阶非线性边值问题,证明了正解的存在性.     

边界元法在地下水补给量计算中的应用

本文是边界元法在地下水补给量计算中应用的一次尝试,它成功地把边界元法应用到考虑有垂向补给或排泄的实际水文地质问题中。文中详细地推导了考虑有垂向补给或排泄均质各向同性承压含水层非稳定流边界元法的计算公式,结合长春市八里堡群井开采试验的水位观测资料计算了河流边界的补给量;分析了目前边界元法在水文地质计算中出现的时间积分和面积积分问题,在这两个问题的解决上做了些改进;结合简单水文地质模型给出了边界元法的精确度。     

基于共轭梯度搜索的病态问题处理方法

在最小二乘平差准则基础上,把病态平差问题转化为无约束的二次规划问题,并利用优化理论分析病态对平差解的影响。通过共轭梯度搜索算法在可行域中寻找最优步长因子,自动寻找最速下降方向,并给出迭代初值的设置方法。分析近似计算中病态问题与局部最优解的关系,讨论局部最优解的快速迭代方法,并通过实例验证算法的有效性,计算迭代的速度。由于整个过程没有对法方程系数矩阵进行求逆计算,该算法可用于处理大规模系数矩阵高病态的平差问题。     

计算Darcy流速时第一类边界的处理

提出了一种求解Darcy流速时一类边界的处理方法.该法利用有限元方程得出一类边界节点的水力坡度和渗流速度,并且模拟了一个理想算例,结果显示解析解与数值解吻合地很好,这表明了该法的有效性.     

Dissipative Travelling Wave Solution for EI Ni(n)o Tropic Sea-air Coupled Oscillator

El Ni(n)o and Southern Oscillation(ENSO)is an interannual phenomenon involved in the tropical Pacific sea-air interactions.An asymptotic method of solving equations for the ENSO model is proposed.Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration,the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied.Firstly,by introducing a set of functionals and computing the variationals,the Lagrange multipliers are obtained.And then,the generalized variational iteration expressions are constructed.Finally,by selecting appropriate initial iteration,and from the iterations expressions,the approximations of solution for the sea-air oscillator ENSO model are solved successively.The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied.It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pa-cific of the sea-air oscillator for ENSO model.     

基于实四元数的大旋转角三维坐标转换的改进谱修正迭代解法

提出一种基于单位实四元数的大旋转角三维坐标转换病态问题的新方法,该方法用单位实四元数构造旋转矩阵,可避免复杂的三角函数求导,易于线性化,系数矩阵更为简洁;考虑到模型法方程矩阵的病态性,引入岭参数和泛函矩阵,从而降低了方程病态性带来的不利影响,使方程求解达到稳定,同时方程迭代求解时解的估计值接近真值的程度较谱修正迭代法高。利用模拟及实测数据对算法进行验证,结果表明,该算法具有收敛速度快、不依赖转换参数初值、全局收敛、解为无偏、便于程序实现等优点,可为通用坐标转换提供一种新途径。     

Blasius问题临界值β~＊的一个新上界

为了研究流体力学边界层理论中的Blasius问题临界值上界的性质,给出了Blasius问题的等价奇异积分方程,通过研究等价的奇异积分方程的正解来研究Blasius问题临界值β＊的上界.通过选用新的比较函数c（t）和g（β）来研究奇异积分方程在C[β,1]中解的存在性,证明所获得的正解是等价奇异积分方程的解,得到Blasius问题临界值的新上界β＊≤-0.1971,改进了最近的首次估计β＊〈-0.18773.     

解扩散方程初边值问题的数值边界元积分方程法

在应用中(如数值天气预报等),经常需要对时空偏微分方程进行数值求解,通常大多采用有限差分计算或有限元法,虽然它们是应用得最广的数值解法(如差分方法),但也有某些局限和不足,本文提出了一种边界元积分方程法。作为示例,我们对扩散方程的初边值问题进行了基本原理和方法的讨论,其基本思想是通过积分变换,消除对时间的依赖性,再在变换空间中,用边界元法对积分后的方程进行数值处理,最后用数值逆变换以完成该问题的数值求解,本方法可对更为复杂的依赖于时间的方程进行类似处理,它具有不同于传统有限差分法和有限单元法特点的优越性,可供有关工作者解初边值问题试用和参考。