Solution of stochastic groundwater flow by infinite series,and convergence of the one-dimensional expansion

This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted . The solution method is based on a Taylor series expansion in terms of parameter , around the value =0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the -expansion solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An infinite-order stochastic solution is obtained in the form of a -power series that converges for any finite value of . It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.     

Optimal nonlinear excitation of decadal variability of the North Atlantic thermohaline circulation

Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation （THC） is investigated with a three-dimensional ocean circulation model, using the conditional nonlinear optimal perturbation method. The results show two types of optimal initial perturbations of sea surface salinity, one associated with freshwater and the other with salinity. Both types of perturbations excite decadal variability of the THC. Under the same amplitude of initial perturbation, the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation, suggesting that the THC is more sensitive to freshwater than salinity perturbation. As the amplitude of initial perturbation increases, the decadal variations become stronger for both perturbations. For salinity perturbations, recovery time of the THC to return to steady state gradually saturates with increasing amplitude, whereas this recovery time increases remarkably for freshwater perturbations. A nonlinear （advective） feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation. The results are consistent with previous ones from simple box models, and highlight the importance of nonlinear feedback in decadal THC variability.     

Perturbations of the upper atmosphere in the cleft region

In the dayside polar region—loosely referred to as the cleft region—particle precipitation and Joule heating cause significant perturbations of the upper atmosphere. Here Dynamics Explorer-2 satellite data are used to present a synopsis of these disturbance effects. Documented are an increase in electron temperature and a decrease in electron density; increases in ion drift speed and ion temperature; an increase in the upward-directed ion velocity; increases in zonal wind speed and neutral gas temperature; and changes in the neutral gas composition and mass density. It is suggested that the increase in electron temperature is partly controlled by the decrease in electron density; that the ion upflow velocity mainly depends on the electron temperature, less frequently on the ion temperature; and that the observed decrease in thermospheric mass density is due to a decrease in the atomic oxygen density, which in turn is caused by diverging wind flows.     

http://www.sciencedirect.com/science/article/pii/S1674987110000368

In this paper,we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes.Associating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods.This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral depos...     

河流流场数值模拟初始场误差发展研究

为分析河流初始场误差对计算结果的影响,利用小扰动方法推导了流动模拟过程中初始场误差发展的控制方程,并依照湖泊假潮的形式得到了方程的分析解。理论结果表明,在通常的边界条件下,初始场误差相当于在流动中附加了一个虚拟的长波,这种波动以驻波的形式存在于河流中,波长是河段长度的4倍,波周期可用梅立恩公式近似估计。在底摩擦的作用下,误差波将会迅速衰减直至消失,充分显示了流场的强耗散特性。通过数值计算实例验证了理论分析的结果。     

权重平衡有向网络下分布式约束优化的连续时间算法设计

本文研究权重平衡有向网络下分布式约束优化问题的求解,其中网络的全局目标函数是由每个智能体的局部目标函数的和构成,全局的约束是由每个智能体的局部约束的交构成.为了分布式求解该问题的最优解,首先引入智能体的局部共轭函数将其转换为Fenchel对偶问题.其次,从Fenchel对偶问题出发,提出一类基于奇异摄动系统的分布式连续时间算法.在局部目标函数和其梯度分别满足强凸和Lipschitz（李普希兹）连续的情况下,结合凸分析方法和Lyapunov（李雅普诺夫）稳定性理论,结果表明所提算法能够获得原问题和对偶问题的最优值.最后,数值仿真进一步验证了所提算法的有效性.     

Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique

A singular perturbation analysis based on the WKB technique to study the hydrodynamic performance of periodic ocean waves that are incident on an open parabolic channel of constant depth is proposed. We derive a linear model to predict the propagation of the long ocean waves into the channel. In this manner, the spatial distribution for the surface elevation of the ocean waves inside the channel as a function of two dimensionless parameters, namely, a kinematical parameter, κ and a geometrical parameter ε, is governed by a second-order ordinary differential equation. The kinematical parameter κ denotes the ratio of the potential head, due to gravity, to the kinetic head of the ocean waves along the longitudinal axis of the parabolic channel. Meanwhile, ε is a dimensionless geometrical parameter that represents a characteristic ratio of the parabolic channel. Using matching conditions, simple expressions for the reflection and transmission coefficients are obtained.     

基于BGM框架的短期集合预报扰动典型规律研究

采用增长模培育(Breeding of Growing Modes,BGM)法开展有限区域模式短期集合预报研究,亟需解决的问题是集合预报扰动的发展及演变。因此论文结合经典的适时缩放培育思想,利用增长模培育法,基于WRF3.6模式(采用WRF-ARW),开发和构建了一个包含水平风场、垂直速度、位温扰动、位势扰动和水汽混合比共6个基本物理量的区域短期集合预报系统(WRF-EPS)。在此基础上,以2016年6月整月我国南方大范围暴雨为样例,针对扰动发展与演变的典型问题进行了探讨。试验结果表明:1)模式大气高、中、低三层的物理量扰动增长可以分为两个阶段,第一阶段为扰动快速线性增长,该阶段内扰动快速完成全部涨幅;第二阶段为非线性稳定阶段,从快速线性增长过渡到非线性稳定阶段大约需要24 h。2)各物理量的扰动增长率、相关系数以及增长模进入非线性稳定阶段的时间大致相同,但对于同一等压面不同物理量或同一物理量不同等压面,每个参数达到非线性稳定后的数值大小及演变规律存在差异,且随时间演变均伴有日内振荡现象。3)对于扰动振幅相同但初始随机模态不同的初值集合,不同随机模态对扰动培育的影响主要是在扰动的非线性稳定阶段,而在快速的线性增长阶段,它们之间的差异很小。4)对于初始随机模态相同但振幅不同的初值集合,不同扰动振幅对扰动演变的影响主要是在扰动的快速线性增长阶段,而在非线性稳定阶段,它们之间的差异很小,并且不同初始振幅对扰动进入非线性稳定阶段的时间基本没有影响。     

Investigation of Motion of Two Hinged Bodies Moored by Mooring Lines in Waves

In this paper, the motions are studied of a multi-body which is composed of two plates hinged together and moored by eight mooring lines in regular waves. The experimental results are compared with computational results. The linear po-tential theory and the perturbation method are combined to study this complicated system. The former is used to calculate the wave forces acting on the plates and the motion responses of them, while the latter is used to describe the dynamic character of the eight mooring lines coupled with the two hinged plates. Some response results of each plate are presented and comparisons between calculated results and experimental data are given. All the calculations are confined to regular beam waves.