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.     

PROPAGATION OF 30—60 DAY LOW FREQUENCY OSCILLATIONS AND THEIR INFLUENCE UPON THE SUBTROPICAL WESTERLIES JET STREAM DURING NORTHERN HEMISPHERE WINTER

Based on daily ECMWF gridpoint data of two winters during 1981—1983 including an ENSOyear,propagation of low frequency oscillations(LFO)during Northern Hemisphere winters andtheir influences upon 30—60 day oscillations of the subtropical jet stream are studied with the sta-tistical methods as complex empirical orthogonal function(CEOF)and so on.Results show that inthe winter of a normal year(1981—1982),30—60 day oscillations in the subtropical zone aremainly in the northern and southern flanks of exit region of jet stream.In the ENSO year(1982—1983),they are mainly in the vicinity of entrance and exit regions of jet stream.Intraseasonalchanges of subtropical jet stream manifested themselves as latitudinal fluctuation or longitudinalprogression or regression of about 40 day period.There are marked differences between propagat-ing passages of low frequency modes responsible for changes of subtropical jet stream in the normalyear(1981—1982)and in the ENSO year(1982—1983).Changes of oscillation amplitude showobvious phases.In general,the one in late winter is stronger than that in early winter,strongestone occurs in February.     

A MESO-β SCALE SIMULATION OF THE EFFECTS OF BOREAL FOREST ECOSYSTEM ON THE LOWER ATMOSPHERE

Based on the Intensive Field Campaign(IFC-1)data of Boreal Ecosystem-Atmosphere Study(BOREAS).a three-dimensional meso-β scale model is used to simulate the effect of boreal forests onthe lower atmosphere.A fine horizontal resolution of 2 km×2 km is used in order to distinguish thevegetative heterogeneity in the boreal region.A total of 20×25 grid points cover the entire sub-modeling area in BOREAS' South Study Area(SSA).The ecosystem types and their coverage ineach grid square are extracted from the North American Land Cover Characteristics Data Base(NALCCD)generated by the U.S.Geographical Survey(USGS)and the University of Nebraska-Lincoln(UNL).The topography of the study area is taken from the Digital Elevation Map(DEM)of USGS.The model outputs include the components of the energy balance budget within the canopyand at the ground.the turbulence parameters in the atmospheric boundary layer and the wind.temperature and humidity profiles extending up to a height of 1500 m.In addition to the fine timeand spatial step,the unique feature of the present model is the incorporation of both dynamic andbiological effects of the Boreal forest into the model parameterization scheme.The model resultscompare favorably with BOREAS' IFC-1 data in 1994 when the forest was in the luxuriant growingperiod.     

Hard X-ray spectrum of Mkn 421 during the active phase

Spectral measurement of Mkn 421 were made in the hard X-ray energy band of 20–200 keV using a high sensitivity, large area scintillation counter telescope on November 21, 2000 and these coincided with the onset of an active X-ray phase as seen in the ASM counting rates on board RXTE. The observed spectrum can not be fitted to a single power law similar to the PDS data of BeppoSAX. The data can be fitted both by a two component power-law function or a combination of an exponential function with a power law component at the high energies above 80 keV. We identify these components with those arising from the synchrotron self compton and the high energy power-law tail arising from the upgrading of the thermal photons due to multiple Compton scattering a la Cyg X-1. A comparison with the earlier data clearly suggests a spectral variability in the hard X-ray spectrum of the source. We propose a continuously flaring geometry for the source as the underlying mechanism for energy release.     

The Dependence of Water Exchanges between the Kuroshio Water and Its Surroundings on the Characteristics of the Kuroshio‘s Meanders

Observation of fluid parcel pathways in the Kuroshio Stream revealed a striking crossstream pattern associated with the Kuroshio‘‘ s meanders. In order to understand the observed pattern, a two-dimensional kinematic model of a meandering jet was developed which could be used to examine the relationship between streamfunction patterns and fluid parcel trajectories. The experiments designed to investigate the dependence of the water exchanges between the Kuroshio water and its surroundings on the characteristics of the Kuroshio‘‘s meanders involved the downstream speed,phase speed and the amplitude of other propagating waves. The results suggested that fluid parcels could cross the meandering jet to and fro; and that the water exchanges between the Kuroshio and its surroundings increased with a) increasing meander amplitude, b) decreasing downstream speed, and c) increasing wave phase speed. The results also showed that when the meandering jet was disturbed by other propagating waves, more effective water exchanges could be induced.     

射电喷流中湍动阿耳芬波对相对论电子的加速

本文通过数值求解带电粒子与Ａｌｆｖｅｎ波湍动相互作用的动力学方程，得到了相对论电子在射电喷流中被加速随时间演化的解．高能电子可以加速到Ｌｏｒｅｎｔｚ因子γｙ～１０６，且形成稳态的幂律谱，尽管其谱指数Ｓ≈ｌ比观测值小，但粒子加速时间约为１０１２－１０１４秒，小于射电斑的寿命１０７年．粒子能谱指数几乎与Ａｌｆｖｅｎ波谱指数和能量损失函数无关．能量损失对加速上限有较大影响．     

Studying Hydrodynamic Instability Using Shock-Tube Experiments

The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.     

沃克环流上升区赤道低空强西风带的分析

采用ＴＯＧＡ／ＣＯＡＲＥ国际合作考察期间（１９９２年１０月─１９９３年２月）获得的２６７次定点（２°Ｓ，１５５°Ｅ）定时高空大气探测资料，进行计算分析，发现１９９２年１２月─１９９３年２月低空存在一支西风急流，有两次分别持续半月之久，而１９９２年１１月的两次赤道西风急流，因无赤道高空急流配合，仅持续２ｄ便消失。本文还指出：（１）赤道低空西风急流是各种海－气指数产生ＥＮＳＯ异常的重要信息；（２）赤道高空急流有滞后赤道低空急流２ｄ左右的响应关系；（３）赤道低空急流是纬向水汽输送的狭窄通道。     

Three-dimensional Layer-integrated Modelling of Estuarine Flows with Flooding and Drying

Details are given of the refinement and application of a thee-dimensional (3-D) layer-integrated numerical model of tidal circulation, with the aim of simulating severe tidal conditions for practical engineering applications. The mode splitting strategy has been used in the model. A set of depth-integrated 2-D equations are first solved to give the pressure gradient, and the layer-integrated 3-D equations are then solved to obtain the vertical distributions of the flow velocities. Attention has been given to maintaining consistency of the physical quantities derived from the 2-D and 3-D equations. A TWO=layer mixing length turbulence model for the vertical shear stress distribution has been included in the model. Emphasis has been focused on applying the model to a real estuary, which is geometrically complicated and has large tidal ranges giving rise to extensive flooding and drying. The model has been applied to three examples, including: wind-driven flow in a rectangular lake, tidal circulation in a model rectangular harbour, and tidal circulation in a large estuary. Favourable results have been obtained for both the simple and complex flow beds.     

天然感潮河道水流紊动特性分析

采用多谱勒三相流速仪，在长江口徐六泾水文观测断面分别进行了涨潮、落潮时中泓与近岸垂线的流速观测，根据这些观测资料，对天然感潮河段潮流紊动的周期、频率、概率密度函数等进行了定量的数学描述，并对时均流速、紊动强度、雷诺应力等沿垂线分布进行了分析计算。