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.     

A Taylor basis for kinematic nonlinear real-time simulations. Part II: The Taylor basis

Real-time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real-time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co-ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co-ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co-ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.     

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.     

Evaluation of evapotranspiration models over semi‐arid and semi‐humid areas of China

Evapotranspiration (ET) is a critical component in the hydrological cycle. However, its actual values appear to be difficult to obtain, especially in areas in which precipitation has high inter‐annual variability. Here, we evaluated eight commonly used ET models in semi‐arid and semi‐humid areas of China. The order of overall performance from best to worst is as follows: the revised Priestley–Taylor model (PT‐JPL, 0.71, 1.65 [18.37%], 4.72 [49.19%]) a a Statistics (model abbreviation, coefficient of determination, bias [relative value], standard deviation [relative value]).
, the modified PT‐JPL model (M1‐PT‐JPL, 0.67, ?0.68 [7.56%], 3.87 [40.31%]), the Community Land Model (CLM, 0.68, ?2.52 [28.01%], 5.10 [53.17%]), the modified PT‐JPL model (M2‐PT‐JPL, 0.63, 0.57 [6.27%], 5.04 [52.52%]), the revised Penman–Monteith model (RS‐PM, 0.62, 3.56 [37.40%], 6.11 [63.68%]), an empirical model (Wang, 0.59, ?1.04 [11.57%], 5.61 [58.43%]), the advection‐aridity model (AA, 0.55, 5.56 [61.78%], 7.45 [77.60%]), and the energy balance model (SEBS, 0.35, 5.11 [56.72%], 9.43 [98.18%]). The performance of all of the models is comparably poor in winter and summer, except for the PT‐JPL model, and relatively good in spring and autumn. Because of the vegetation control on ET, the Wang, RS‐PM, PT‐JPL, M1‐PT‐JPL, and M2‐PT‐JPL models perform better for cropland, whereas the AA model, SEBS model and CLM perform better for grassland. The CLM, PT‐JPL, and Wang models perform better in semi‐arid region than in semi‐humid region, whereas the opposite is true for SEBS and RS‐PM. The AA, M1‐PT‐JPL, and M2‐PT‐JPL models perform similarly in semi‐arid and semi‐humid regions. When considering the inter‐annual variability in precipitation, the Wang model has relatively good performance under only some annual precipitation conditions; the performance of the PT‐JPL and AA models is reduced under conditions of high precipitation; the two modified PT‐JPL models inherited the steady performance of the PT‐JPL model and improved the performance under conditions of high annual precipitation by the modification of the soil moisture constraint. RS‐PM is more appropriate for humid conditions. CLM and PT‐JPL models could be effectively applied to all precipitation conditions because of their good performance across a wide annual precipitation range. Copyright © 2016 John Wiley & Sons, Ltd.     

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。     

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.     

基于CHAMP卫星与三维Taylor多项式模型的区域地磁建模研究

利用CHAMP卫星矢量和标量地磁测量数据,通过三维Taylor多项式模型建立了2010.0年中国及邻近地区在300km高度附近的X、Y、Z和F分量的三维磁场模型.为了比较验证所建模型,分析了其与Taylor多项式模型(二维模型)不同截断阶数所对应的均方偏差(RMSE)、残差及分布等.结果表明,三维模型每一阶的RMSE和残差绝对值的平均值均要比二维模型的小约45%.由于采用了系数完全展开的建模方式,三维模型的系数数量约为二维模型的2倍,三维模型较低的截断阶数可以反映更多的地磁信息.本研究中的5阶三维Taylor模型基本可达到8阶Taylor模型的精度.两种模型绘制的地磁场及残差分布有较好的一致性.     

球层中高阶自由热对流格局及其变化的研究

研究了下边界为应力自由边界, 上边界为刚性边界, 纯粹从底部加热的充满了无穷大普朗特数的Boussinesq流体的同心球层中的非线性自由热对流. 借鉴将极型场和扰动温度场展成勒让德多项式（以下称零级数模型, 即此时m=0）的方法, 将它们展成6阶6级（即l=6; m=0, 1, 2, hellip;, l）的勒让德函数（以下称高级数模型）, 并用Galerkin方法求解非线性方程组, 获得了高级数模型的结果. 与零级数模型仅能获得表征物质垂直运移特征和扰动温度结构的二维南北向（rphi;）剖面相比, 高级数模型还得到了东西向（rphi;）和深度剖面（theta;phi;）, 而且对流运动的许多细特征得以体现, 有利于深化认识球层中自由热对流的特征及其导致的温度结构. 瑞利数的大小对自由热对流的格局和速率产生了重要的影响, 控制着对流层中高温热柱区和低温冷柱区的相对大小. 本文所得到的结果可能主要反映了下地幔物质运动, 其对流格局和速率在不同的位置上存在明显的差异, 可能蕴涵了重要的地球动力学含义.      

波浪场中浓度输移扩散Stokes漂移效应的欧拉描述

为了说明波浪场中浓度输移扩散Stokes漂移效应的欧拉描述方法,采用欧拉方法推导了波浪场中波浪周期平均的浓度输移扩散方程,其对流项是由波浪速度的波动和物质浓度的波动相互作用而产生,所含的对流速度恰是Stokes漂移速度。由此说明,波浪场中浓度扩散问题的Stokes漂移效应可以自动的由欧拉法来考虑,所得到的Stokes漂移效应与拉格朗日描述的结果是等价的。为了进一步说明这一问题,将粒子追踪法的拉格朗日描述的Stokes漂移速度与欧拉法的结果进行了对比,二者是一致的。研究中也数值求解了线性波浪场中σ坐标下浓度扩散方程,将浓度的Stokes漂移、浓度分布和粒子追踪法的结果进行了对比,以证明欧拉描述和拉格朗日描述两种方法的等价性。研究中也根据实验结果对实际波浪场中Stokes漂移效应所引起的浓度漂移进行了讨论,解释了物理模型实验中的观察到的波浪场中浓度漂移现象。     

Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

A predictor‐multicorrector implementation of a Time Discontinuous Galerkin method for non‐linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed‐form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor‐multicorrector algorithm for different approximations of non‐linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright © 2002 John Wiley & Sons, Ltd.