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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.
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
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Continuous wavelet analyses of hourly time series of air temperature, stream discharge, and precipitation are used to compare the seasonal and inter‐annual variability in hydrological regimes of the two principal streams feeding Bow Lake, Banff National Park, Alberta: the glacial stream draining the Wapta Icefields, and the snowmelt‐fed Bow River. The goal is to understand how water sources and flow routing differ between the two catchments. Wavelet spectra and cross‐wavelet spectra were determined for air temperature and discharge from the two streams for summers (June–September) 1997–2000, and for rainfall and discharge for the summers of 1999 and 2000. The diurnal signal of the glacial runoff was orders of magnitude higher in 1998 than in other years, indicating that significant ice exposure and the development of channelized glacial drainage occurred as a result of the 1997–98 El Niño conditions. Early retreat of the snowpack in 1997 and 1998 led to a significant summer‐long input of melt runoff from a small area of ice cover in the Bow River catchment; but such inputs were not apparent in 1999 and 2000, when snow cover was more extensive. Rainfall had a stronger influence on runoff and followed quicker flow paths in the Bow River catchment than in the glacial catchment. Snowpack thickness and catchment size were the primary controls on the phase relationship between temperature and discharge at diurnal time scales. Wavelet analysis is a fast and effective means to characterize runoff, temperature, and precipitation regimes and their interrelationships and inter‐annual variability. The technique is effective at identifying inter‐annual and seasonal changes in the relative contributions of different water sources to runoff, and changes in the time required for routing of diurnal meltwater pulses through a catchment. However, it is less effective at identifying changes/differences in the type of the flow routing (e.g. overland flow versus through flow) between or within catchments. Copyright © 2003 John Wiley & Sons, Ltd. 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
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1 .IntroductionThe lifting systemis composed of pipes andtheir connectors .It is not onlythe lifting channel formanganese nodule betweenthe miningship andintermediate bin,but alsothe supporting massfor deepsea miningequipment and cables .Sothe reliability… 相似文献
6.
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
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