On the modified Taylor constraint

A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe magnetic field generation in Earth’s core well, a magnetostrophic dynamo has not yet been found even though Taylor [Proc. R. Soc. Lond. A 1963, 274, 274–283] devised an apparently viable method of finding one. His method for determining the fluid velocity from the magnetic field and the energy source involved only the evaluation of integrals along lines parallel to the Earth’s axis of rotation and the solution of a second-order ordinary differential equation. It is demonstrated below that an approximate solution of this equation for a broad family of magnetic fields is immediate. Furthermore inertia, which was neglected in Taylor’s theory, is restored here, so that the modified theory includes torsional waves, whose existence in the Earth’s core has been inferred from observations of the length of day. Their theory is reconsidered.     

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.     

The Helium Isotopic Chemistry of Lake Bonney, Taylor Valley, Antarctica: Timing of Late Holocene Climate Change in Antarctica

To better understand the long-term climate history of Antarctica, we studied Lake Bonney in Taylor Valley, Southern Victoria Land (78°S). Helium isotope ratios and He, Ne, Ar and N₂ concentration data, obtained from hydrocasts in the East (ELB) and West (WLB) Lobes of Lake Bonney, provided important constraints on the lakes Holocene evolution. Based on very low concentrations of Ar and N₂ in the ELB bottom waters, ELB was free of ice until 200 ± 50 years ago. After which, low salinity water flowing over the sill from WLB to ELB, covered ELB and formed a perennial ice cover, inhibiting the exchange of gases with the atmosphere. In contrast to the ELB, the WLB retained an ice cover through the Holocene. The brine in the WLB bottom waters has meteoric N₂ and Ar gas concentrations indicating that it has not been significantly modified by atmospheric exchange or ice formation. The helium concentrations in the deep water of WLB are the highest measured in non-thermal surface water. By fitting a diffusional loss to the ³He/⁴He, helium, and Cl profiles, we calculate a time of 3000 years for the initiation of flow over the sill separating the East and West Lobes. To supply this flux of helium to the lake, a helium-rich sediment beneath the lake must be providing the helium by diffusion. If at any time during the last million years the ice cover left WLB, there would be insufficient helium available to provide the current flux to WLB. The variations in water levels in Lake Bonney can be related to climatic events that have been documented within the Southern Victoria Land region and indicate that the lakes respond significantly to regional and, perhaps, global climate forcing.     

PREDICTION AND UNCERTAINTY OF CLIMATE CHANGE IN CHINA DURING 21ST CENTURY UNDER RCPS

Based on integrated simulations of 26 global climate models provided by the Coupled Model Intercomparison Project(CMIP), this study predicts changes in temperature and precipitation across China in the 21 st century under different representative concentration pathways(RCPs), and analyzes uncertainties of the predictions using Taylor diagrams. Results show that increases of average annual temperature in China using three RCPs(RCP2.6, RCP4.5,RCP8.5) are 1.87 ℃, 2.88 ℃ and 5.51 ℃, respectively. Increases in average annual precipitation are 0.124, 0.214, and 0.323 mm/day, respectively. The increased temperature and precipitation in the 21 st century are mainly contributed by the Tibetan Plateau and Northeast China. Uncertainty analysis shows that most CMIP5 models could predict temperature well, but had a relatively large deviation in predicting precipitation in China in the 21 st century. Deviation analysis shows that more than 80% of the area of China had stronger signals than noise for temperature prediction;however, the area proportion that had meaningful signals for precipitation prediction was less than 20%. Thus, the multi-model ensemble was more reliable in predicting temperature than precipitation because of large uncertainties of precipitation.     

减弱热带气旋附近的倾斜涡度发展

根据1998年北半球夏季6、7、8月逐月500hPa高度场实测资料,利用具有双重筛选功能的二维空间谱分析方法,分别获得了能大致反映1998年北半球6、7、8月500hPa高度场分布特征的3组空间波集,每组包含15个空间波。分别利用这3组空间谱函数,从Galerkin途径出发,获得了1998年长江流域夏季降水异常的一个物理机制:在前期典型ElNi?o型海温异常,以及5月后ElNio型海温异常减弱,Lania型海温异常分布建立的这些外部异常热力强迫作用下,导致大气环流出现不同的非线性内部动力过程,6月大气环流演变中波波相互作用和波流相互作用较弱,7、8月的大气环流演变中尽管波波相互作用明显,但波流相互作用仍然很弱。波流相互作用的持续偏弱,导致了1998年夏季西太平洋副热带高压位置持续偏南,夏季强降雨带持续稳定于长江流域。     

含单个孔洞岩盐路基稳定性的无网格分析

用无网格伽辽金法计算了孔洞边缘危险点的应力。对含单个孔洞岩盐路基的稳定性进行了分析,给出了针对不同孔洞埋深的临界载荷。数值结果表明,EFGM对于解决含有单个孔洞的应力集中问题,是有效且灵活的。     

利用改进泰勒级数法对磁异常场进行向下延拓

基于高精度的磁异常场垂向导数,提出采用改进泰勒级数法实现磁异常场的向下延拓。通过仿真试验数据对提出的向下延拓方法进行了验证,结果表明,该方法可实现磁异常场稳健向下延拓,其计算精度要优于目前常用的傅里叶变换法和常规泰勒级数法计算精度。     

Roughness scale dependence of the relationship between tracer longitudinal dispersion and Peclet number in variable‐aperture fractures

The relationship between the longitudinal dispersion (D_L) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the D_L and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the D_L from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the D_L and Pe revealed that the longitudinal dispersivity α_L increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of α_L and the secondary roughness played a significant role in enhancing the α_L. As the Taylor dispersion mechanism dominated, the α_L was insensitive to the influence of multiscale roughness in variable‐aperture fractures.     

渗流场随机性的随机有限元分析

基于一阶Taylor随机有限元法,推导出相应的渗流场随机分析中渗流响应量（水头和水力梯度）的随机响应公式,进而实现三维稳定渗流场随机有限元分析,并编制了相应的程序。在分析中,将渗流区域材料的渗透张量视为三维各向异性随机场,利用三维可分离向量随机场的局部平均法对随机场进行离散,根据参数选取的不同,可以离散出不同数量的随机变量。最后,给出一个算例,对离散出随机变量数量不同的情况分别进行随机分析,将分析结果和仅仅将渗透张量视为三维随机变量得到的结果对比,验证了所提方法的可行性。     

中国地区地磁长期变化研究

采用2000~2004年中国地区34个台站的地磁日均值数据, 计算了通日和静日的平均年变率,以及静日的拟合年变率.应用上述年变率, 建立了2000.0~2005.0年代中国地区地磁场长期变化泰勒多项式模型和曲面样条模型.分析讨论了该泰勒多项式模型和曲面样条模型与国际地磁参考场长期变化模型(IGRF-SV)的异同, 结果表明,中国地区地磁长期变化的泰勒多项式模型与曲面样条模型的形态与数值是一致的,而且与IGRF-SV长期变化的趋势也是一致的,但中国地区地磁长期变化具有区域特征.