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1.
Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock
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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
2.
Janis Britals 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):305-316
It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy. 相似文献
3.
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
4.
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, TL, 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 TLand the escape time, TE, 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 TE=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 TLandTE is found. 相似文献
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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
7.
Sebastiano Calvo Gianfranco Lovison Maria Pirrotta Germana Di Maida Agostino Tomasello & Mariangela Sciandra 《Marine Ecology》2006,27(4):361-371
The relationship between flowering and growth performance of Posidonia oceanica (L.) Delile in meadows distributed along the south‐eastern coast of Sicily (Italy) was investigated by means of a statistical model (generalized linear mixed model) combined with the lepidochronological analysis. Over a 28‐year period, 67 floral stalk remains were observed. The highest flowering index was recorded in lepidochronological year 1998 (10.1%) and the Inflorescence Frequency per age showed a clear decrease corresponding to 15‐year‐old shoots. The sexual reproductive event had positive effects on rhizome elongation (cm year?1) and leaf production (no. leaves year?1) in the same flowering year, whilst no effect on the rhizome production (mg year?1) was observed. Rhizome growth variables showed significant negative lagged responses in the two years following flowering. On the whole, we calculated that the effect exerted by flowering, in terms of loss on rhizome elongation and production, was about 27% and 38%, respectively. Although it has been demonstrated that recovery from the stress induced by sexual reproduction is limited to the two years after flowering, the magnitude of the reproductive cost may become quite considerable especially in comparison with the whole lifespan of individual shoots. 相似文献
8.
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
9.
刘新国 《中国海洋大学学报(自然科学版)》1988,(2)
本文讨论几类特殊的矩阵多项式,先介绍几个基本概念,然后证明。对这几类特殊的矩阵多项式,与之相应的L—值问题可转化为低次的代数多项式求根问题。最后,使用“投影尺度”建立了L—值的摄动定理。 相似文献
10.