Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

长江上游洪涝暴雨环流形势中期演变趋势分析

本文通过对1980年以来长江上游10次洪涝过程的500hpa环流形势分析,并用车比雪夫多项式对500hpa高度场进行展开,研究了各类洪涝过程的中期演变特征,发现代表不同洪涝过程环流形势变化的不同的车氏系数值都有明显的特征变化,结合欧洲中心中期数值预告96小时500hpa高度场的车氏系数分析,可为洪涝暴雨的中期预报提供一种新的思路。     

过渡季节(6—7月)澳大利亚冷高压对赤道辐合带形成的影响

应用车贝雪夫多项式分析过渡季节(6—7月)澳大利亚冷高压与赤道辐合带的关系,得出了对赤道辐合带北移的主要形势以及过程演变特征,最后用合成方法得到它的演变概念模式,为赤道辐合带的北移影响西太平洋及南海地区提供了中期预报的依据。     

白沙河地下水资源管理模型

针对白沙河地下水含水层的内部结构和本区开采特点以及已出现的环境问题，建立了地下水资源管理模型，确定了优化开采方案。该管理模型针对本区每年２个管理时段的长度及其开采量均不同的特点，导出了新的响应矩阵的公式。管理模型的建立有助于对该区地下水的合理开采。     

渤、黄、东海底摩擦系数的研究

本文将伴随法用于渤、黄、东海M2分潮的数值模拟,利用Topex／Poseidon高度计资料进行同化,优化海底摩擦系数。文中对底摩擦系数取常数时进行了优化,同时还对底摩擦系数的一种新的处理方法进行了研究,即在计算海区选取一些点给定底摩擦系数,海区中任意一点的底摩擦系数由这些点的底摩擦系数线性播值得到,优化后得到空间分布的底摩擦系数。针对两种不同的线性底摩擦假设分别进行了一系列的实际实验,结果表明由空间分布的底摩擦系数得到的模拟值比底摩擦系数取常数得到的模拟值更接近观测值,能有效地提高数值模拟的精度。     

关于多项式特征值的条件数

Tisseur(2000)研究了非齐次多项式特征值问题的条件数，所得结果的不足是对无穷特征值必须另外处理；Declieu和Tisseur(2003)运用微分几何方法研究了齐次多项式特征值问题的条件数，所得结果的不足之处是与系数矩阵的尺度化(scaling)有关。这两种条件数都有各自的应用范围。本文基于投影尺度引入齐次多项式特征值问题的条件数，其优点是与系数矩阵的尺度化无关，因而也许会有较广泛的应用。     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

浅述多元数据处理的一种简化拟合形式及算法剖析

在实际工程试验与研究中 ,多元数据处理经常遇到 ,根据 Weierstrass定理 ,采用多项式拟合是一种常见的数据处理方法。对于多元多项式的系数求解问题 ,可以归结为超定方程组的求解问题。该文以超定方程组的 SVD求解算法为核心 ,阐述了在工程实际中关于多元数据处理的一种应用方法 ,并尝试给出多元多项式拟合的一种简化方法     

浮体间距对多浮体系统水动力系数的影响

根据三维线性势流理论，采用格林函数法，对多浮体系统的水动力系数进行了数值分析。数值算例中给出了在固定波频下水动力系数与浮体间相对位置关系曲线。水动力系数的变化幅度随着浮体间距离增大而变小。随着浮体间距的变化，水动力系数极值的出现具有明显的规律，相邻的极大值(或极小值)的间距为半个波长或一个波长。     

Performance of hemi-cylindrical and rectangular submerged breakwaters

A parametric experimental study is conducted to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. The results show that, for the rigid breakwaters, rectangular models are more effective than hemi-cylindrical ones in terms of reduction of transmitted waves. As for the flexible breakwaters, the hemi-cylindrical models may give better wave reflection than rectangular ones. However, the energy loss induced by the rectangular breakwaters is much larger and more significant to result in an overall better efficiency in terms of reduction in wave transmission. The effects of internal pressure show that the lowest pressurized flexible models considered in this work are the most effective in the reduction of the transmitted wave height. Higher wave reflection, lower wave transmission and higher energy loss are obtained consistently at the lower submergence depth ratio.