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1.
Most river cross-sections display some degree of asymmetry for which there is no adequate quantitative definition. Indices of asymmetry are derived using two principles based on areal differences and maximum depth displacement relative to the channel centreline. The indices are assessed firstly by comparing values for a set of constructed channel shapes which are ranked in order of increasing visual asymmetry, and secondly by analysing a series of 50 cross-sections from a small mountain stream. Two indices, A* and A2, are probably the most valuable, and could be used to test and generate hypotheses regarding the related changes to cross-sectional and planimetric form which occur during the transition from a straight to a meandering channel, particularly if parallel measures of flow asymmetry are defined. Part II of this paper, concerned with ‘Mode of Development and Local Variation’ will be published in a subsequent issue of this journal.  相似文献   

2.
Alternative indices of cross-section asymmetry are compared. Observed values of two preferred indices for 567 natural sections across eleven confined upland channels are predictably low along such low sinuosity reaches. Variation in asymmetry of sections located around confined, unconfined but stable, and freely-migrating bends is evaluated. Consideration of the influence of bed topography emphasizes local plan curvature of bed forms as an important control on degree of asymmetry. Variation in indices for bed forms in similar planform locations indicates the levels of asymmetry at different stages of the transformation of channel geometry over time.  相似文献   

3.
针对现有的河道水流洪水演算模型只能模拟单一变量(流量或水位)的问题,以水流连续方程和河段蓄水量的两种不同表达形式(蓄水量等于平均过水断面面积与河段长乘积,蓄水量等于河段平均流量与传播时间的乘积)为基础,对马斯京根模型进行了通用性改进,提出了双变量耦合通用演算模型.选取了四大水系(包括内陆河流和入海河流)的16个河段汛期洪水资料进行模型检验,模型验证考虑了地理范围、不同的河段特征和水力特征、洪水量级等因素,全面地检验了模型结构的合理性和模拟实际洪水的有效性.将双变量耦合通用演算模型与传统的马斯京根法进行了效果比较,结果表明双变量耦合通用演算模型的模拟精度高于马斯京根法,模拟效果比马斯京根法稳定一些,而且具有较好的通用性.  相似文献   

4.
Spatial prediction of river channel topography by kriging   总被引：2，自引：0，他引：2  
Topographic information is fundamental to geomorphic inquiry, and spatial prediction of bed elevation from irregular survey data is an important component of many reach‐scale studies. Kriging is a geostatistical technique for obtaining these predictions along with measures of their reliability, and this paper outlines a specialized framework intended for application to river channels. Our modular approach includes an algorithm for transforming the coordinates of data and prediction locations to a channel‐centered coordinate system, several different methods of representing the trend component of topographic variation and search strategies that incorporate geomorphic information to determine which survey data are used to make a prediction at a specific location. For example, a relationship between curvature and the lateral position of maximum depth can be used to include cross‐sectional asymmetry in a two‐dimensional trend surface model, and topographic breaklines can be used to restrict which data are retained in a local neighborhood around each prediction location. Using survey data from a restored gravel‐bed river, we demonstrate how transformation to the channel‐centered coordinate system facilitates interpretation of the variogram, a statistical model of reach‐scale spatial structure used in kriging, and how the choice of a trend model affects the variogram of the residuals from that trend. Similarly, we show how decomposing kriging predictions into their trend and residual components can yield useful information on channel morphology. Cross‐validation analyses involving different data configurations and kriging variants indicate that kriging is quite robust and that survey density is the primary control on the accuracy of bed elevation predictions. The root mean‐square error of these predictions is directly proportional to the spacing between surveyed cross‐sections, even in a reconfigured channel with a relatively simple morphology; sophisticated methods of spatial prediction are no substitute for field data. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

5.
Riffle‐pool sequences are a common feature of gravel‐bed rivers. However, mechanisms of their generation and maintenance are still not fully understood. In this study a monitoring approach is employed that focuses on analysing cross‐sectional and longitudinal channel geometry of a large floodplain river (Vereinigte Mulde, Sachsen‐Anhalt, Germany) with a high temporal and spatial resolution, in order to conclude from stage‐dependant morphometric changes to riffle and pool maintaining processes. In accordance with previous authors, pool cross‐sections of the Mulde River are narrow and riffle cross‐sections are wide suggesting that they should rather be addressed as two general types of channel cross‐sections than solely as bedforms. At high flows, riffles and pools in the study reaches changed in length and height but not in position. Pools were scoured and riffles aggraded, a development which was reversed during receding flows below the threshold of 0·4Qbf (40% bankfull discharge). An index for the longitudinal amplitude of riffle‐pool sequences, the bed undulation intensity or bedform amplitude, is introduced and proved to be highly significant as a form parameter, its first derivative as a process parameter. The process of pool scour and riffle fill is addressed as bedform maintenance or bedform accentuation. It is indicated by increasing longitudinal bed amplitudes. According to the observed dynamics of bed amplitudes, maintenance of riffle‐pool sequences lags behind discharge peaks. Maximum bed amplitudes may be reached with a delay of several days after peak discharges. Increasing bed undulation intensity is interpreted to indicate bed mobility. Post‐flood decrease of the bed undulation intensity indicates a retrograde phase when transport from pools to riffles has ceased and bed mobility is restricted to riffle tails and heads of pools. This type of transport behaviour is referred to as disconnected mobility. The comparison of two river reaches, one with undisturbed sediment supply, the other with sediment deficit, suggests that high bed undulation intensity values at low flows indicate sediment deficit and potentially channel degrading conditions. It is more generally hypothesized that channel bed undulations constitute a major component of form roughness and that increased bed amplitudes are an important feature of channel bed adjustment to sediment deficit be it temporally during late floods or permanently due to a supply limitation of bedload. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

6.
We present new in situ observations of systematic asymmetry in the pattern of damage expressed by fault zone rocks along sections of the San Andreas, San Jacinto, and Punchbowl faults in southern California. The observed structural asymmetry has consistent manifestations at a fault core scale of millimeters to meters, a fault zone scale of meters to tens of meters and related geomorphologic features. The observed asymmetric signals are in agreement with other geological and geophysical observations of structural asymmetry in a damage zone scale of tens to hundreds of meters. In all of those scales, more damage is found on the side of the fault with faster seismic velocities at seismogenic depths. The observed correlation between the damage asymmetry and local seismic velocity structure is compatible with theoretical predictions associated with preferred propagation direction of earthquake ruptures along faults that separate different crustal blocks. The data are consistent with a preferred northwestward propagation direction for ruptures on all three faults. If our results are supported by additional observations, asymmetry of structural properties determined in field studies can be utilized to infer preferred propagation direction of large earthquake ruptures along a given fault section. The property of a preferred rupture direction can explain anomalous behavior of historic rupture events, and may have profound implications for many aspects of earthquake physics on large faults.  相似文献   

7.
To enhance the utilization efficiency of farmland irrigation water and reduce the leakage of water conveyance channels, the leakage process of channels was simulated dynamically. The simulated results were compared with data measured in laboratory experiments, and the performance of the model was evaluated. The results indicated that the simulated values of the model were consistent with the observation values, and the R2 values varied between 0.91 and 0.99. In addition, based on the laboratory experiments, a water supply system (Mariotte bottles) and soil box were built using plexiglass. Three influencing factors, namely, the channel form, soil texture and channel cross-sectional area, were varied to observe and calculate the resulting cumulative infiltration amount, infiltration rate and wetting front migration distance. HYDRUS-3D software was used to solve the three-dimensional soil water movement equation under different initial conditions. The results demonstrated that the U-shaped channel was more effective than the trapezoidal channel in increasing the utilization efficiency of the water resources. A U-shaped channel with a small channel cross-sectional area should be adopted and the soil particle size should be prioritized in the construction of water conveyance channels for farmlands. The simulation results were in agreement with the observed results, which indicates that HYDRUS-3D is a reliable tool that can accurately simulate the soil moisture movement in water conveyance channels. The research results can provide a reference for the design and operation of farmland irrigation systems.  相似文献   

8.
A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.  相似文献   

9.
A number of methods and formulae has been proposed in the literature to estimate the discharge capacity of compound channels. When the main channel has a meandering pattern, a reduction in the conveyance capacity for a given stage is observed, which is due to the energy dissipations caused by the development of strong secondary currents and to the decrease of the main channel bed slope with respect to the valley bed slope. The discharges in meandering compound channels are usually assessed applying, with some adjustments, the same methods used in the straight compound channels. Specifically, the sinuosity of the main channel is frequently introduced to account for its meandering pattern, although some methods use different geometric parameters.In this paper the stage—discharge curves for several compound channels having identical cross-sectional area, roughness and bed slope but different planimetric patterns are numerically calculated and compared, in order to identify which geometric parameter should be efficaciously used in empirical formulae to account for meandering patterns. The simulations are carried out using a 3D finite-volume model that solves the RANS equations using a k-ε turbulence model. The numerical code is validated against experimental data collected in both straight and meandering compound channels.The numerical results show that the sinuosity is the main parameter to be accounted for in empirical formulae to assess the conveyance capacity of meandering compound channels. Comparison of the stage—discharge curves in the meandering compound channels with that obtained in a straight channel having identical cross-sectional area clearly shows the reduction of discharge due to the presence of bends in the main channel. The effect of other geometric parameters, such as the meander-belt width and the mean curvature radius, results very weak.  相似文献   

10.
Erosion processes in bedrock‐floored rivers shape channel cross‐sectional geometry and the broader landscape. However, the influence of weathering on channel slope and geometry is not well understood. Weathering can produce variation in rock erodibility within channel cross‐sections. Recent numerical modeling results suggest that weathering may preferentially weaken rock on channel banks relative to the thalweg, strongly influencing channel form. Here, we present the first quantitative field study of differential weathering across channel cross‐sections. We hypothesize that average cross‐section erosion rate controls the magnitude of this contrast in weathering between the banks and the thalweg. Erosion rate, in turn, is moderated by the extent to which weathering processes increase bedrock erodibility. We test these hypotheses on tributaries to the Potomac River, Virginia, with inferred erosion rates from ~0.1 m/kyr to >0.8 m/kyr, with higher rates in knickpoints spawned by the migratory Great Falls knickzone. We selected nine channel cross‐sections on three tributaries spanning the full range of erosion rates, and at multiple flow heights we measured (1) rock compressive strength using a Schmidt hammer, (2) rock surface roughness using a contour gage combined with automated photograph analysis, and (3) crack density (crack length/area) at three cross‐sections on one channel. All cross‐sections showed significant (p < 0.01 for strength, p < 0.05 for roughness) increases in weathering by at least one metric with height above the thalweg. These results, assuming that the weathered state of rock is a proxy for erodibility, indicate that rock erodibility varies inversely with bedrock inundation frequency. Differences in weathering between the thalweg and the channel margins tend to decrease as inferred erosion rates increase, leading to variations in channel form related to the interplay of weathering and erosion rate. This observation is consistent with numerical modeling that predicts a strong influence of weathering‐related erodibility on channel morphology. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

11.
Regression equations with the form y = f(q), where y is a channel characteristic and q is a discharge of a particular frequency are widely used in fluvial geomorphology. They imply that channel geometry is related to a dominant discharge. For this to be so, the river must be ‘in regime’ i.e. its characteristics must fluctuate about a mean condition which is effectively stationary at the time scale considered. The static regression-dominant discharge approach does not fully describe the relationship between channel characteristics and discharge and an alternative model is proposed with the form y(t) = ∞ h(u)- q(t-u)du. This model states that channel form is a product of the whole series of discharges experienced by the channel. The dominant discharge-static regression approach provides a working approximation of the relationship between channel characteristics and discharge only when temporal variations in q are small or when y is insensitive to variations in q.  相似文献   

12.

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams.

Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).

  相似文献   

13.
D. W. Crowder  P. Diplas   《Journal of Hydrology》2000,230(3-4):172-191
Modeling of flow features that are important in assessing stream habitat conditions has been a long-standing interest of stream biologists. Recently, they have begun examining the usefulness of two-dimensional (2-D) hydrodynamic models in attaining this objective. Current modeling practices consider relatively long channel sections with their bathymetry represented in terms of large, macro-scale, topographic features. Meso-scale topographic features, such as boulders, root-wads and other obstructions are typically not considered in the modeling process. Instead, the overall effects of these flow obstructions are captured through increased values in the channel roughness parameters. Such an approach to 2-D modeling allows one to accurately predict average depth and velocity values; however, it is not capable of providing any information about the flow patterns in the vicinity of these obstructions. Biologists though have known that such meso-scale features and the complex velocity patterns generated by their presence, play an important role in the ecology of streams, and thus cannot be ignored. It is therefore evident that there is a need to develop better tools, capable of modeling flow characteristics at scales of ecological importance. The purpose of this study is to expand the utility of 2-D hydraulic models to capture these flow features that are critical for characterizing stream habitat conditions.

There exists a paucity of research addressing what types of topographic features should be included in 2-D model studies and to what extent a boulder or series of exposed boulders can influence predicted flow conditions and traditional useable habitat computations. Moreover, little research has been performed to evaluate the impact mesh refinement has on model results in natural streams. Numerical simulations, based on a natural river channel containing several large boulders, indicate that explicitly modeling local obstructions/boulders can significantly impact predicted flow parameters. The presence of these obstructions create velocity gradients, velocity shelters, transverse flows and other ecologically important flow features that are not reproduced when their geometry is not incorporated into the hydraulic model. Sensitivity analyses show that reducing element sizes in the vicinity of obstructions and banks is crucial in modeling the spatial flow patterns created by meso-scale topographic features. This information, combined with similar data obtained in future studies, can provide guidelines for the placement of fishrocks and other structures often used in stream restoration projects as well as determining what types of meso-scale topographic features might need to be incorporated into habitat suitability studies. Such information may also ultimately allow new spatial habitat metrics to be developed.  相似文献   


14.
Stream power can be an extremely useful index of fluvial sediment transport, channel pattern, river channel erosion and riparian habitat development. However, most previous studies of downstream changes in stream power have relied on field measurements at selected cross‐sections, which are time consuming, and typically based on limited data, which cannot fully represent important spatial variations in stream power. We present here, therefore, a novel methodology we call CAFES (combined automated flood, elevation and stream power), to quantify downstream change in river flood power, based on integrating in a GIS framework Flood Estimation Handbook systems with the 5 m grid NEXTMap Britain digital elevation model derived from IFSAR (interferometric synthetic aperture radar). This provides a useful modelling platform to quantify at unprecedented resolution longitudinal distributions of flood discharge, elevation, floodplain slope and flood power at reach and basin scales. Values can be resolved to a 50 m grid. CAFES approaches have distinct advantages over current methodologies for reach‐ and basin‐scale stream power assessments and therefore for the interpretation and prediction of fluvial processes. The methodology has significant international applicability for understanding basin‐scale hydraulics, sediment transport, erosion and sedimentation processes and river basin management. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

15.
Non-linear tidal dynamics are investigated in a network that consists of a semi-enclosed main channel and a secondary channel at an arbitrary position. The water motion, governed by the one-dimensional shallow water equations, is forced by an incoming tidal wave. Solutions are obtained with the method of characteristics. The overall aim is to quantify and understand the spatial structure of different tidal harmonics (the principal tide and its non-linear overtides) and of tidal asymmetry for both the vertical and the horizontal tide in the main channel for different locations of the secondary channel. This is of practical interest in the context of possible construction of secondary channels to reduce tidal range in estuaries. Moreover, tidal asymmetry is an important factor in driving net sediment transport. Analysis of the different tidal harmonics shows that their characteristics are similar to those obtained with an earlier linear model. In particular, amplitudes of the harmonics are reduced landward of the secondary channel if the latter is positioned less than a quarter wavelength of the respective tidal wave away from the landward boundary. Thus, the distortions of the tide due to the presence of the secondary channel are generated locally and afterwards propagate through the network. Tidal asymmetry is quantified by examining tidal range, flood-to-ebb ratio and the duration of the falling tide and the duration between maximum flood and maximum ebb. A spatial non-uniform reduction in tidal range is observed that shows very localised increase and decrease depending on the position of the secondary channel. The changes in the velocity characteristics induce changes in net sediment transport. It turns out that the direction of the peak current, derived from the flood-to-ebb ratio, is not sensitive to the position of the secondary channel, whereas the duration between flood and ebb can change from more to less than half the tidal cycle. However, the changes in the velocity asymmetries are confined to a small region.  相似文献   

16.
The discharge hydrograph estimation in rivers based on reverse routing modeling and using only water level data at two gauged sections is here extended to the most general case of significant lateral flow contribution, without needing to deploy rainfall–runoff procedures. The proposed methodology solves the Saint‐Venant equations in diffusive form also involving the lateral contribution using a “head‐driven” modeling approach where lateral inflow is assumed to be function of the water level at the tributary junction. The procedure allows to assess the discharge hydrograph at ends of a selected river reach with significant lateral inflow, starting from the stage recorded there and without needing rainfall data. Specifically, the MAST 1D hydraulic model is applied to solve the diffusive wave equation using the observed stage hydrograph at the upstream section as upstream boundary condition. The other required data are (a) the observed stage hydrograph at the downstream section, as benchmark for the parameter calibration, and (b) the bathymetry of the river reach, from the upstream section to a short distance after the downstream gauged section. The method is validated with different flood events observed in two river reaches with a significant intermediate basin, where reliable rating curves were available, selected along the Tiber River, in central Italy, and the Alzette River, in Luxembourg. Very good performance indices are found for the computed discharge hydrographs at both the channel ends and along the tributaries. The mean Nash‐Sutcliffe value (NSq) at the channel ends of two rivers is found equal to 0.99 and 0.86 for the upstream and downstream sites, respectively. The procedure is also validated on a longer stretch of the Tiber River including three tributaries for which appreciable results are obtained in terms of NSq for the computed discharge hydrographs at both the channel ends for three investigated flood events.  相似文献   

17.
We study how a coastal obstruction (peninsula or coastal island) affects the three-dimensional barotropic currents in an oblong rectangular basin with variable bathymetry across the basin width. The transverse depth profile is asymmetric and the peninsula or island lies in the middle of the long side of the rectangle. A semi-spectral model for the Boussinesq-approximated shallow water equations, developed in Haidvogel et al. and altered for semi-implicit numerical integration in time in Wang and Hutter, is used to find the steady barotropic state circulation pattern to external winds. The structural (qualitative) rearrangements and quanti2tative features of the current pattern are studied under four principal wind directions and different lengths of the peninsula and its inclination relative to the shore. The essentially non-linear relationships of the water flux between the two sub-basins (formed by the obstructing peninsula) and the corresponding cross-sectional area left open are found and analysed. It is further analysed whether the depth-integrated model, usually adopted by others, is meaningful when applied to the water exchange problems. The flow through the channel narrowing is quantitatively estimated and compared with the three-dimensional results. The dynamics of the vortex structure and the identification of the up-welling/down-welling zones around the obstruction are discussed in detail. The influence of the transformation of the peninsula into a coastal island on the global basin circulation is considered as are the currents in the channel. The geometric and physical reasons for the anisotropy of the current structure which prevail through all obtained solutions are also discussed.Dedicated to Professor L.A. Mysak on the occasion of his sixtieth birthday.  相似文献   

18.
Simple stability relationships are practically useful to provide a rapid assessment of coastal and estuarine landforms in response to human interventions and long‐term climate change. In this contribution, we review a variety of simple stability relationships which are based on the analysis of tidal asymmetry (TA). Most of the existing TA‐based stability relationships are derived using the one‐dimensional tidal flow equations assuming a certain regular shape of the tidal channel cross‐sections. To facilitate analytical solutions, specific assumptions inevitably need to be made, for example by linearizing the friction term and dropping some negligible terms in the tidal flow equations. We find that three major types of TA‐based stability relationships have been proposed between three non‐dimensional channel geometric ratios (represented by the ratio of channel widths, ratio of wet surface areas and ratio of storage volumes) and the tide‐related parameter a/h (i.e. the ratio between tidal amplitude and mean water depth). Based on established geometric relations, we use these non‐dimensional ratios to restate the existing relationships so that they are directly comparable. Available datasets are further extended to examine the utility of these TA‐based relationships. Although a certain agreement is shown for these relationships, we also observe a large scatter of data points which are collected in different types of landscape, hydrodynamic and sedimentological settings over the world. We discuss in detail the potential reasons for this large scatter and subsequently elaborate on the limited applicability of the various TA‐based stability relationships for practical use. We highlight the need to delve further into what constitutes equilibrium and what is needed to develop more robust measures to determine the morphological state of these systems. Copyright © 2018 John Wiley & Sons, Ltd.  相似文献   

19.
Electrokinetic phenomena in a water-porous medium with a fractal structure above percolation threshold are theoretically investigated. Fracture zone with space-variable porosity is considered as a model of an earthquake hypocenter zone in which the electrokinetic current results from fluid filtration in a fractal pore network. A critical exponent of the streaming potential coefficient is found to depend on both the transport critical exponent and correlation length critical exponent. In this model, logarithmic dependence of electric field amplitude E on the earthquake magnitude M is derived which is compatible with the one observed by the VAN group. Without fractal properties, this form of dependence contradicts the empirical data. The electromagnetic field far from the hypocenter is calculated, which leads to the prediction of weak magnetic field variations. To explain the observed amplitude of VAN's Seismic Electric Signals (SES), the electric source must be at a distance of about 10 km from the registration point if the medium is homogeneous. Therefore, some conductive channel(s) are needed to explain the long distance selective SES transmission.  相似文献   

20.
The scattering behaviour of bullet-rosette and bullet-shaped ice particles is investigated using model calculations (ray tracing method) with special emphasis on the asymmetry factor g. Because the variability of the geometrical features of these particles is very large, some representative shapes are used in the calculations. The model is based on geometrical optics, and particles are assumed to be oriented randomly; a wavelength of 0.56 m is considered; absorption is neglected. The scattering behaviour of bullet rosettes is compared to that of single branches out of the bullet rosette. It turns out that there are slight differences in the asymmetry factor values, depending on the lengths of the branches (g\approx0.02) and on the angles between the branches (g\approx0.01). Bullets show some special features in their phase functions due to the pyramid. The length of the particle influences the asymmetry factor (g\approx0.10), as does the shape of the pyramid (g\approx0.07). The influence of the pyramidal shape decreases with increasing particle length. Bullets were compared to hexagonally shaped columns. This was done for two columns, one as long as the columnar part of the bullet (length without pyramid), and one for a column as long as the bullet including the pyramid. Asymmetry factor values of bullets with a pyramidal angle of 28° deviate less than g\approx0.01 from the range given by the two values of the columns.  相似文献   

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