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.     

Flows in clumpy planetary nebulae

The dynamics of clumps observed in planetary nebulae are considered. The possibility that SiO maser spots in evolved stars and the planetary nebula clumps are formed by the Parker instability behind shocks in pulsating stars' atmospheres is raised. Molecular observations of the clumps are suggested. The effects of the ablation of clumps on the global flow structure of a more tenuous plasma in which they are embedded are reviewed.     

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.     

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.     

Hydrogeological framework and water balance studies in parts of Krishni–Yamuna interstream area, Western Uttar Pradesh, India

The Krishni–Yamuna interstream area is a micro-watershed in the Central Ganga Plain and a highly fertile track of Western Uttar Pradesh. The Sugarcane and wheat are the major crops of the area. Aquifers of Quaternary age form the major source of Irrigation and municipal water supplies. A detailed hydrogeological investigation was carried out in the study area with an objective to assess aquifer framework, groundwater quality and its resource potential. The hydrogeological cross section reveals occurrence of alternate layers of clay and sand. Aquifer broadly behaves as a single bodied aquifer down to the depth of 100 m bgl (metre below ground level) as the clay layers laterally pinch out. The depth to water in the area varies between 5 and 16.5 m bgl. The general groundwater flow direction is from NE to SW with few local variations. An attempt has been made to evaluate groundwater resources of the area. The water budget method focuses on the various components contributing to groundwater flow and groundwater storage changes. Changes in ground water storage can be attributed to rainfall recharge, irrigation return flow and ground water inflow to the basin minus baseflow (ground water discharge to streams or springs), evapotranspiration from ground water, pumping and ground water outflow from the basin. The recharge is obtained in the study area using Water table fluctuation and Tritium methods. The results of water balance study show that the total recharge in to the interstream region is of the order of 185.25 million m³ and discharge from the study area is of the order of 203.24 million m³, leaving a deficit balance of −17.99 million m³. Therefore, the present status of groundwater development in the present study area has acquired the declining trend. Thus, the hydrogeological analysis and water balance studies shows that the groundwater development has attained a critical state in the region.     

Risk assessment strategies for the reactivation of earth flows in the Northern Apennines (Italy)

The aim of this paper is to analyze the reactivation mechanism of ancient earth flows, with a view to gleaning information that can subsequently be utilized to formulate a risk-reduction strategy. All considerations made herein are the result of direct experience and observation of actual events which have occurred over the past few decades in the Northern Apennines. Particular attention has been paid to the analysis of the evolution of landslides during actual reactivation, acknowledging a typical, recurring succession of events that precede the failure of the slope. The hazard assessment of these large landslide bodies, which are of slope scale, constitutes a thorny problem, especially in view of the inapplicability of traditional deterministic models such as limit equilibrium stability analysis. Nevertheless, a site-specific assessment of probability of reactivation of these large and ancient earth flows is fundamental to effective land-use planning.     

Deep-seated gravitational slope deformations and their influence on consequent mass movements (case studies from the highest part of the Czech Carpathians)

Gravitational spreading of mountain ridges displays primary disequilibrium of flysch mountain areas of the Czech Carpathians. The progression of various types of mass movements is a product of long-term ridge disintegration and is predisposed by the geological structure of the area and the upper Tertiary-Quaternary morphogenesis of the mountain area. Deep-seated slope deformations are spatially interconnected by the occurrence of some other types of slope deformations (e.g. debris flows, debris slides, slumps, rock avalanches, etc.), which pose a considerable risk for the existence of human society. An important causative factor in these dynamically developing hazardous processes is, among other factors, the way in which land has been used in the last three centuries. Therefore, the occurrence of various types of slope deformations is studied in terms of their relation to deep-seated gravitational deformations and in terms of other limiting factors (structural geological, morphological and climatic factors, manmade impacts, etc.). The paper presents several case studies of slope deformations (Velká Čantoryje Mt, Lysá hora Mt, Ropice Mt and Smrk Mt) in the area of the Outer Carpathians within the territory of the Czech Republic and also adverts to some consequences in terms of the socioeconomic structure of the landscape.     

Rain-induced debris and mudflow triggering factors assessment in the Santiago cordilleran foothills,Central Chile

Debris and mudflows are some of the main geological hazards in the mountain foothills of the Chilean capital city of Santiago. There, the risk of flows triggered in the basins of ravines that drain the range into the city increases with time due to the city growth. A multivariate statistical study based on the logistic regression method is presented. The model provides equations that allow the computation of combined meteorological triggering factors associated with a probability of rain-induced flow occurrence. Daily rainfall, accumulated rainfall and the snowfall level, traditionally considered as the relevant factors, are analysed for a 25-year period. The results show a strong relevance of the rainfall on the day of the flow event over the other factors. However, the relatively low probabilities returned for some real flow events suggest that the model does not capture all the significant variables and the problem is more complex than as it has been traditionally assumed, and further investigations are needed to develop predictive models of flow triggering.     

The spatial implications of the functional proximity deriving from air passenger flows between European metropolitan urban regions

Until recently the traditional spatial configuration of the European geography was based upon the core-periphery model. The ‘pentagon’, broadly defined as lying between London, Paris, Milan, Munich and Hamburg, was seen as the core area characterised by having the highest concentration of economic development in the European Union (EU), with the remainder of the European territory viewed as peripheral, albeit to varying degrees. In a number of cases such peripheral areas equated with clear regional disparities. The elaboration of the European Spatial Development Perspective (ESDP) (CEC, European spatial development perspective, towards balanced and sustainable development in the territory of the European Union, 1999) challenged this core-periphery model. European spatial planning policies, aimed at encouraging social and economic, and with ever increasing importance, territorial cohesion, seek amongst other aspects to encourage the development of a balanced and polycentric urban system. This paper adopts a network analysis approach to the analysis of air passenger flows between some 28 principal European metropolitan urban regions. The evaluation of these flows contributes to an enhanced comprehension of the spatial dynamics of the European metropolitan territory which goes beyond that deriving from the more standard analyses of the individual components of the urban system. Several indicators are used, deriving from gravitational modelling techniques, to analyse the complexity of the air passenger flows. A multidimensional scaling (MDS) technique is introduced in order to interpret and visualise the resulting spatial configuration and positioning of the different metropolitan centres within the conceptual European ‘space of air passenger flows’, thereby contrasting with the more traditional map-based geographical image of Europe, based upon Cartesian coordinates.