Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

一种从经纬度网格资料获得正方形网格资料的插值方案

本文提出了一种把经纬度网格点上的气象要素值转化到正方形网格点上的多项式插值方案。对插值方案作了稳定性讨论和定量及定性分析。结果表明,这种插值方案方便可行,而且有广泛适用性。     

Numerical calculations in the orbital determination of an artificial satellite for a long arc

Numerical methods are usually used for the computation of ephemerides with perturbations for the precise orbital determination of an artificial satellite. But their numerical stability will be encountered in a long arc. In this case the use the improved Encke special perturbation methods has been suggested. The results of this paper show that Encke's method does indeed have a certain effectiveness, but cannot yet completely resolve the numerical stability, and the more efficient method is to use the energy integral or its variational relation to control the growth of the along-track error in general numerical calculations so that the aim of stabilization can be achieved.     

A numerical method for differential equations of second order

A new algorithm of order five is presented for the solution of the initial value problem where the system of ordinary differential equations is of second order and does not contain the first derivative.     

Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target

2D numerical modelling of impact cratering has been utilized to quantify an important depth-diameter relationship for different crater morphologies, simple and complex. It is generally accepted that the final crater shape is the result of a gravity-driven collapse of the transient crater, which is formed immediately after the impact. Numerical models allow a quantification of the formation of simple craters, which are bowl-shaped depressions with a lens of rock debris inside, and complex craters, which are characterized by a structural uplift. The computation of the cratering process starts with the first contact of the impactor and the planetary surface and ends with the morphology of the final crater. Using different rheological models for the sub-crater rocks, we quantify the influence on crater mechanics. To explain the formation of complex craters in accordance to the threshold diameter between simple and complex craters, we utilize the Acoustic Fluidization model. We carried out a series of simulations over a broad parameter range with the goal to fit the observed depth/diameter relationships as well as the observed threshold diameters on the Moon, Earth and Venus.     

Alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands)

Ancient fluvial successions often act as hydrocarbon reservoirs. Sub‐surface data on the alluvial architecture of fluvial successions are often incomplete and modelling is performed to reconstruct the stratigraphy. However, all alluvial architecture models suffer from the scarcity of field data to test and calibrate them. The purposes of this study were to quantify the alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands) and to determine spatio‐temporal trends in the architecture. Five north–south orientated cross‐sections, perpendicular to the general flow direction, were compiled for the fluvial‐dominated part of the delta. These sections were used to calculate the width/thickness ratios of fluvial sandbodies (SBW/SBT) and the proportions of channel‐belt deposits (CDP), clastic overbank deposits (ODP) and organic material (OP) in the succession. Furthermore, the connectedness ratio (CR) between channel belts was calculated for each cross‐section. Distinct spatial and temporal trends in the alluvial architecture were found. SBW/SBT ratios decrease by a factor of ca 4 in a downstream direction. CDP decreases from ca 0·7 (upstream) to ca 0·3 (downstream). OP increases from less than 0·05 in the upstream part of the delta to more than 0·25 in the downstream delta. ODP is approximately constant (0·4). CR is ca 0·25 upstream, which is approximately two times larger than in the downstream part of the delta. Furthermore, CDP in the downstream Rhine–Meuse delta increases after 3000 cal yr BP. These trends are attributed to variations in available accommodation space, floodplain geometry and channel‐belt size. For instance, channel belts tend to narrow in a downstream direction, which reduces SBW/SBT, CDP and CR. Tectonics cause local deviations in the general architectural trends. In addition, the positive correlation between avulsion frequency and the ratio of local to regional aggradation rate probably influenced alluvial architecture in the Rhine–Meuse delta. The Rhine–Meuse data set can be a great resource when developing more sophisticated models for alluvial architecture simulation, which eventually could lead to better characterizations of hydrocarbon reservoirs. To aid such usage of the Rhine–Meuse data set, constraints for relevant parameters are provided at the end of the paper.     

Morphological analysis of the drainage system in the Eastern Alps

We study the morphology of the major rivers draining the Eastern Alps to test whether the active tectonics of this part of the orogen is reflected in the shape of channel profiles of the river network. In our approach we compare channel profiles measured from digital elevation models with numerically modelled channel profiles using a stream power approach. It is shown that regions of high stream power coincide largely with regions of highest topography and largest uplift rates, while the forelands and the Pannonian Basin are characterised by a significantly lower stream power. From stream power modelling we conclude that there is young uplift at the very east of the Eastern Alps, in the Bohemian Massif and in the Pohorje Range. The impact of the Pleistocene glaciations is explored by comparing properties of rivers that drain in proximal and distal positions relative to the ice sheet during the last glacial maximum. Our analysis shows that most knick points, wind gaps and other non-equilibrium features of catchments covered by ice during the last glaciations (Salzach, Enns) can be correlated with glacial processes. In contrast the ice free catchments of the Mur and Drava are characterized by channels in morphological equilibrium at the first approximation and are showing only weak evidence of the strong tectonic activity within these catchments. Finally, the channel profiles of the Adige and the divide between the upper Rhine and Danube catchments differ significantly from the other catchments. We relate this to the fact that the Adige and the Rhine respond to different base levels from the remainder of the Eastern Alps: The Adige may preserve a record from the Messininan base level change and the Rhine is subject to the base level lowering in the Rhine Graben.     

Numerical modeling for analyzing thermal surface anomalies induced by underground coal fires

Coal seams burning underneath the surface are recognized all over the world and have drawn increasing public attention in the past years. Frequently, such fires are analyzed by detecting anomalies like increased exhaust gas concentrations and soil temperatures at the surface. A proper analysis presumes the understanding of involved processes, which determine the spatial distribution and dynamic behavior of the anomalies.In this paper, we explain the relevance of mechanical and energy transport processes with respect to the occurrence of temperature anomalies at the surface. Two approaches are presented, aiming to obtain insight into the underground coal fire situation: In-situ temperature mapping and numerical simulation. In 2000 to 2005, annual temperature mapping in the Wuda (Inner Mongolia, PR China) coal fire area showed that most thermal anomalies on the surface are closely related to fractures, where hot exhaust gases from the coal fire are released. Those fractures develop due to rock mechanical failure after volume reduction in the seams. The measured signals at the surface are therefore strongly affected by mechanical processes.More insight into causes and effects of involved energy transport processes is obtained by numerical simulation of the dynamic behavior of coal fires. Simulations show the inter-relation between release and transport of thermal energy in and around underground coal fires. Our simulation results show a time delay between the coal fire propagation and the observed appearance of the surface temperature signal. Additionally, the overall energy flux away from the burning coal seam into the surrounding bedrock is about 30-times higher than the flux through the surface. This is of particular importance for an estimation of the energy released based on surface temperature measurements. Finally, the simulation results also prove that a fire propagation rate estimated from the interpretation of surface anomalies can differ from the actual rate in the seam.     

Migration of the Ganga river and its implication on hydro-geological potential of Varanasi area, U.P., India

Borehole data reveals that during Late Quaternary, the Ganga river was non-existent in its present location near Varanasi. Instead, it was flowing further south towards peripheral craton. Himalayan derived grey micaceous sands were being carried by southward flowing rivers beyond the present day water divide of Ganga and mixed with pink arkosic sand brought by northward flowing peninsular rivers. Subsequently, the Ganga shifted to its present position and got incised. Near Varanasi, the Ganga river is flowing along a NW-SE tectonic lineament. The migration of Ganga river is believed to have been in response to basin expansion caused due to Himalayan tectonics during Middle Pleistocene times. Multi-storied sand bodies generated as a result of channel migration provide excellent aquifers confined by a thick zone of muddy sediments near the surface. Good quality potable water is available at various levels below about 70 m depth in sandy aquifers. Craton derived gravelly coarse-to-medium grained sand forms the main aquifer zones of tens of meter thickness with enormous yield. In contrast, the shallow aquifers made up of recycled interfluve silt and sandy silt occur under unconfined conditions and show water-level fluctuation of a few meters during pre-and post-monsoon periods.     

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC⁺⁺. Examples are provided to demonstrate the new contact rule between two blocks.