Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock          下载免费PDF全文

N. Zolfaghari  E. Dontsov  A. P. Bunger 《国际地质力学数值与分析法杂志》2018,42(4):587-617

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.  相似文献   

长江上游洪涝暴雨环流形势中期演变趋势分析     

郁淑华  骆红  芮良生 《成都信息工程学院学报》1990,(1)

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。  相似文献   

Chaotic Diffusion And Effective Stability of Jupiter Trojans     

Kleomenis Tsiganis  Harry Varvoglis  Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):71-87

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.  相似文献   

地球化学景观吸引子的发现及其意义     

李长江  麻土华  徐有浪 《浙江国土资源》1995,(1)

勘查地球化学对异常评价的最大不确定性源于对地球化学景观特性的认识不够。我们应用构造相空间的方法分析了浙江儒岙幅（1:5万）水系沉积物测量的Ag含量数据，揭示了地球化学景观是具有低维吸引子（DZ≈2．9）的混饨系统。这一发现将对勘查地球化学中采样密度的选择、地球化学场模拟、异常评价等根本性问题产生重大影响。  相似文献   

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     

邓良焱  薛惠娴 《热带海洋学报》1993,(4)

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。  相似文献   

关于多项式特征值的条件数     

刘新国  王学锋 《中国海洋大学学报(自然科学版)》2004,34(5):913-917

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。  相似文献   

一种新型混沌遗传优化算法的研究     

张海燕  潘成欣 《中国海洋大学学报(自然科学版)》2006,36(4):555-558

在对遗传算法交叉、变异后结果的处理方法进行改进并在将进化过程分段的基础上,提出1种新的混沌遗传算法。该算法利用混沌运动的遍历性择优产生初始群体,对每一轮遗传操作所得到的部分当前最优个体进行变尺度混沌搜索。仿真结果表明,该算法具有较高的优化效率,并能求得全局最优解。  相似文献   

浅述多元数据处理的一种简化拟合形式及算法剖析   总被引：1，自引：1，他引：1  

李继刚  陈华秋  徐春红  李杨眉 《海洋技术学报》2002,21(3):1-4

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  相似文献   

Population dynamics of two marine polychaetes: the relative role of density dependence, predation, and winter conditions     

van der Meer  Jaap; Beukema  Jan J; Dekker  Rob 《ICES Journal of Marine Science》2000,57(5):1488-1494

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基于主动轮廓线模型的配准方法     

何乔  李二森  罗继文  张华 《海洋测绘》2007,27(4):28-30

随着地图修测的迫切需要,如何实现影像与地图的精确配准就成为急需解决的问题。虽然多项式模型的配准方法简单直观,但不能满足高精度地图修测的需要。目前影像与矢量图的配准靠人工实现,不容易准确量测,这越来越成为地图修测中全自动空中三角测量的瓶颈。而主动轮廓线模型通过模板自身的弹性形变,与图像局部特征相匹配达到调和,即某种能量函数极小化,从而实现矢量图与影像的精确配准。因此,提出了一种基于B样条Snake模型分割的高精度配准方法。  相似文献