On the stability of stratified plane couette flow

Abstract

Unbounded stratified plane Couette flow is shown to be stable against small amplitude disturbances. The Brunt-Väisälä frequency is assumed to be constant. Both viscosity and thermal diffusion are included, and shown to be stabilizing.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Fractal reconstruction of sea-floor topography

Sea-floor bathymetric profiles exhibit features at many different scales of length; this suggests that they could be described as fractals. An algorithm interpolating a fractal line between points has been used to reconstruct bathymetric profiles from a few data points. In general, this fractal line has the same Fourier amplitude spectrum as real bathymetry, and, if the parameters of the interpolation are suitably chosen, it has a very similar appearance. The success of this fractal reconstruction algorithm for the sea-floor raises the possibility that it could be used to extrapolate, from data collected at one scale, the properties of the sea-floor at finer scales, and that similar techniques could be used to interpolate a surface between bathymetric profiles. The fractal character is a sign that the processes that shape the sea-floor are scale invariant and suggests that the renormalization group technique could be used to model these processes.     

On the modelling of sand bedforms using the semivariogram

This study shows the usefulness of the semivariogram for modelling sand ripples created by water flows of varied flow intensity. A combination of two mathematical functions is fitted to each sample semivariogram, that is an exponential (or stochastic) component and a periodic component. The parameters of each of these components have direct physical meaning. A non-dimensional ratio combining the two parameters of the exponential model is interpreted as a regularity index (which increases with the degree of regularity of bedform arrangement). This regularity index is inversely related to the Froude number of the flow. The non-dimensional wavelength, estimated from the dominant periodic function, is also inversely and closely related to the Froude number. The wave height, accurately estimated from properties of the two fitted components, is a direct function of flow velocity and is also proportional to the standard deviation of bed elevations. The bedform shape introduces a considerable discrepancy between the generally assumed normal frequency distribution and the empirical distributions of bed height. The series of bed elevations are generally characterized by a mixture of normal distributions having the same variance but different means. The calculation of a covariance assuming a constant and single mean (as in spectral analysis) can therefore be misleading and the problem may be avoided by using the semivariogram.     

Statistical distribution of natural fractures and the possible physical generating mechanism

We have fitted field measurements of fracture spacings (from the vicinity of Lake Strom Thurmond, Georgia, U.S.A.) to the Weibull, Schuhmann and fractal distributions. The fracture spacings follow a fractal and Weibull distribution which implies that they were formed as a result of a repetitive fragmentation process. The limited variation of the fracture density with orientation in the study area suggests that the stress distribution generating these fractures may be uniform.     

Prediction of tension crack location and riverbank erosion hazards along destabilized channels

Riverbank erosion, associated sedimentation and land loss hazards are a land management problem of global significance and many attempts to predict the onset of riverbank instability have been made. Recently, Osman and Thorne (1988) have presented a Culmann-type analysis of the stability of steep, cohesive riverbanks; this has the potential to be a considerable improvement over previous bank stability theories, which do not account for bank geometry changes due to toe scour and lateral erosion. However, in this paper it is shown that the existing Osman-Thorne model does not properly incorporate the influence of tension cracking on bank stability since the location of the tension crack on the floodplain is indirectly determined via calculation or arbitrary specification of the tension crack depth. Furthermore, accurate determination of tension crack location is essential to the calculation of the geometry of riverbank failure blocks and hence prediction of land loss and bank sediment yield associated with riverbank instability and channel widening. In this paper, a rational, physically based method to predict the location of tension cracks on the floodplain behind the eroding bank face is presented and tested. A case study is used to illustrate the computational procedure required to apply the model. Improved estimates of failure block geometry using the new method may potentially be applied to improve predictions of bank retreat and floodplain land loss along river channels destabilized as a result of environmental change.     

重磁解释中健全的极大似然法及三维反演

本文介绍了JOAO.B.C.SILVA提出的重磁解释中健全的(Robust)极大似然反演方法的基本原理,讨论了重力二度体非线性几何参数的反演情况,并将该方法扩展到三维重、磁非线性几何参数反演中。重点讨论了场值中有较大随机干扰、有不同类型的地质噪音源影响下的反演结果。理论反演结果表明,该方法有比最小二乘反演方法更接近实际的解,从而提高了解的可靠性,对于重磁局部异常或孤立异常有较好的反演效果。     

Structural pattern in the Precambrian rocks of Sonua-Lotapahar region,North Singhbhum,eastern India

In the western part of the North Singhbhum fold belt near Lotapahar and Sonua the remobilized basement block of Chakradharpur Gneiss is overlain by a metasedimentary assemblage consisting of quartz arenite, conglomerate, slate-phyllite, greywacke with volcanogenic material, volcaniclastic rocks and chert. The rock assemblage suggests an association of volcanism, turbidite deposition and debris flow in the basin. The grade of metamorphism is very low, the common metamorphic minerals being muscovite, chlorite, biotite and stilpnomelane. Three phases of deformation have affected the rocks. The principal D1 structure is a penetrative planar fabric, parallel to or at low angle to bedding. No D1 major fold is observed and the regional importance of this deformation is uncertain. The D2 deformation has given rise to a number of northerly plunging major folds on E-W axial planes. These have nearly reclined geometry and theL ₂lineation is mostly downdip on theS ₂surface, though some variation in pitch is observed. The morphology of D2 planar fabric varies from slaty cleavage/schistosity to crenulation cleavage and solution cleavage. D3 deformation is weak and has given rise to puckers and broad warps on schistosity and bedding. The D2 major folds south of Lotapahar are second order folds in the core of the Ongarbira syncline whose easterly closure is exposed east of the mapped area. Photogeological study suggests that the easterly and westerly closing folds together form a large synclinal sheath fold. There is a continuity of structures from north to south and no mylonite belt is present, though there is attenuation and disruption along the fold limbs. Therefore, the Singhbhum shear zone cannot be extended westwards in the present area. There is no evidence that in this area a discontinuity surface separates two orogenic belts of Archaean and Proterozoic age.     

水系分维的构造含义

本文运用分数维几何学,研究了河流水系分维与地壳里向运动、活动断裂格局及运动学特征的关联性。结果表明:1)地壳垂向运动控制大型河流主干的总体形态;2)活动断裂格局复杂、水平运动强烈的地区,水系分维值高;3)走滑断裂较斜滑断裂对水系发育的控制强烈,而后者主要起到对水系的分区作用。     

地震自相似现象初探

依据破裂过程和震源物理参数相似性,给出了自相似震源椭球体三轴之比约为a:b:c=1:0.2:0.2。基于分维理论和方法,讨论了自相似的地震时空分布的分维和强震前的降维现象。由前兆展布范围,大震前区域地震活动特征以及地震空区等可导出近源前兆(红肿)区线性尺度约为震源区的5倍。