On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part I. Equilibrium turbulent closure models

The weak turbulent motions of a dry granular dense flow and the influence of the turbulent fluctuations caused by the minor short-term elastic/inelastic instantaneous collisions and the major long-term enduring frictional contacts among the grains on the mean flow characteristics are investigated. To this end, the conventional Reynolds-averaging process is applied to obtain the balance equations for the mean primitive fields associated with turbulent closure models. The thermodynamic analysis, based on the Mueller–Liu entropy principle, is carried out to derive the equilibrium formulations of the closure models. It shows that the effect of the turbulent fluctuations on the mean flow characteristics as well as the turbulent kinetic energy and dissipation can be taken into account by the granular coldness: a phenomenological measure of the fluctuating kinetic energy intensity. The implementation of the complete thermodynamically consistent turbulent closure models and the simulation of a gravity-driven stationary flow down an inclined moving plane compared with the experimental outcomes are provided in Part II of the present study.     

石梁河水库消力池强紊动水流的数值模拟

采用半隐式的控制体积法离散紊流控制方程,考虑曲率修正的双方程紊流模型封闭雷诺应力,引入通度和体积函数的概念,数值模拟了石梁河水库工程改建后两级消力池的泄流过程.计算结果给出了自由表面的演变过程及其相互碰撞、重叠的消力池水流特征,断面流速、压力分布及自由水面位置与物理模型试验结果吻合良好.     

淹没水跃的数值模拟

利用标准双方程紊流模型数值模拟了进口Fr₁为819、淹没度为024、闸下出流形成的淹没水跃。详细介绍了数值离散格式特别是用VOF方法跟踪非恒定自由表面的数值方法。将淹没水跃的数值模拟结果包括自由表面位置、平均流速、雷诺应力分量的分布与物模试验结果进行了对比,表明该数学模型及数值方法能够较为准确地模拟淹没水跃的大尺度紊流结构及其微观结构。     

Continuum hydrodynamics of dry granular flows employing multiplicative elastoplasticity

We present a Lagrangian formulation for simulating the continuum hydrodynamics of dry granular flows based on multiplicative elastoplasticity theory for finite deformation calculations. The formulation is implemented within the smoothed particle hydrodynamics (SPH) method along with a variant of the usual dynamic boundary condition. Three benchmark simulations on dry sands are presented to validate the model: (a) a set of plane strain collapse tests, (b) a set of 3D collapse tests, and (c) a plane strain simulation of the impact force generated by granular flow on a rigid wall. Comparison with experimental results suggests that the formulation is sufficiently robust and accurate to model the continuum hydrodynamics of dry granular flows in a laboratory setting. Results of the simulations suggest the potential of the formulation for modeling more complex, field-scale scenarios characterized by more elaborate geometry and multi-physical processes. To the authors’ knowledge, this is the first time the multiplicative plasticity approach has been applied to granular flows in the context of the SPH method.     

Statistical properties of the atmospheric turbulent boundary layer over steep surface waves

A new method of digital optical anemometry (Particle Image Velocimetry, PIV) of turbulent flows is suggested and implemented in the laboratory; it is based on the use of continuous laser radiation and high-speed video photography, providing continuous statistical ensembles of flow velocity fields. Application of the method to the study of wind field over waves has allowed us to perform, for the first time, direct measurements of velocity fields, averaged over turbulent pulsations induced by waves in the air flow. The experiments demonstrated that the velocity fields, averaged over the turbulent pulsations, are nonseparated even in the case of steep and breaking waves, when separation of the flow from the wave crests in the instantaneous fields is observed. Based on comparison with the experimental data, it is shown that the average wind fields over waves are described well quantitatively in the framework of semiempirical closure models of turbulence.     

Limitations and improvements of the energy balance closure with reference to experimental data measured over a maize field

The use of energy fluxes data to validate land surface models requires that energy balance closure conservation is satisfied, but usually this condition is not verified when the available energy is bigger than the sum of turbulent vertical fluxes. In this work, a comprehensive evaluation of energy balance closure problems is performed on a 2012 data set from Livraga obtained by a micrometeorological eddy covariance station located in a maize field in the Po Valley. Energy balance closure is calculated by statistical regression of turbulent energy fluxes and soil heat flux against available energy. Generally, the results indicate a lack of closure with a mean imbalance in the order of 20%. Storage terms are the main reason for the unclosed energy balance but also the turbulent mixing conditions play a fundamental role in reliable turbulent flux estimations. Recently introduced in literature, the energy balance problem has been studied as a scale problem. A representative source area for each flux of the energy balance has been analyzed and the closure has been performed in function of turbulent flux footprint areas. Surface heterogeneity and seasonality effects have been studied to understand the influence of canopy growth on the energy balance closure. High frequency data have been used to calculate co-spectral and ogive functions, which suggest that an averaging period of 30 min may miss temporal scales that contribute to the turbulent fluxes. Finally, latent and sensible heat random error estimations are computed to give information about the measurement system and turbulence transport deficiencies.     

Flow, sediment transport and bedform dynamics over the transition from dunes to upper-stage plane beds: implications for the formation of planar laminae

Preliminary results are reported from an experimental study of the interaction between turbulence, sediment transport and bedform dynamics over the transition from dunes to upper stage plane beds. Over the transition, typical dunes changed to humpback dunes (mean velocity 0–8 ms^-1, depth 01 m, mean grain size 0.3 mm) to nominally plane beds with low relief bed waves up to a few mm high. All bedforms had a mean length of 0.7–0.8 m. Hot film anemometry and flow visualization clearly show that horizontal and vertical turbulent motions in dune troughs decrease progressively through the transition while horizontal turbulence intensities increase near the bed on dune backs through to a plane bed. Average bedload and suspended load concentrations increase progressively over the transition, and the near-bed transport rate immediately downstream of flow reattachment increases markedly relative to that near dune crests. This relative increase in sediment transport near reattachment appears to be due to suppression of upward directed turbulence by increased sediment concentration, such that velocity close to the bed can increase more quickly downstream of reattachment. Low-relief bedwaves on upper-stage plane beds are ubiquitous and give rise to laterally extensive, mm-thick planar laminae; however, within such laminae are laminae of more limited lateral extent and thickness, related to the turbulent bursting process over the downstream depositional surface of the bedwaves.     

Characterization of mesoscale instabilities in localized granular shear using digital image correlation

Within shear bands in sands, deformation is largely non-affine, stemming primarily from buckling of well-known force chains and also from vortex-like structures. In the spirit of current trends toward multiscale modeling, understanding the links between these mesoscale deformational entities and corresponding macroscale response will form the basis for the next generation of sand behavioral models and may also aid in efforts to understand jamming–unjamming transitions in dense granular flows in general. Experimental methods to quantify and characterize such subscale kinematics, in particular in real sands, will play critical roles in these efforts. Digital Image Correlation (DIC) is a fast growing experimental technique to nondestructively measure surface displacements from digital images. Here, DIC has been employed to identify and characterize the development of vortex structures inside shear bands formed in dense sands during plane strain compression. A rigorous assessment of the DIC method has been performed, in particular for subscale behavioral characterization in unbonded granular solids, and guidelines are offered for accurate implementation. While DIC systematically overestimates shear band thickness, a methodology has been devised to compensate for this overestimation. Shear band thickness for four different uniform sands were found to range between 6 and 9 grain diameters, and for a well-graded sand between 8 and 9.5 grain diameters. These determinations agree with visual inspections of grain kinematics from the image data, as well as recent theoretical predictions.     

The vertical turbulence structure of experimental turbidity currents encountering basal obstructions: implications for vertical suspended sediment distribution in non‐equilibrium currents

Large roughness features, caused by erosion of the sea floor, are commonly observed on the modern sea floor and beneath turbidite sandstone beds in outcrop. This paper aims to investigate the effect of such roughness elements on the turbulent velocity field and its consequences for the sediment carrying capacity of the flows. Experimental turbidity currents were run through a rectangular channel, with a single roughness element fixed to the bottom in some runs. The effect of this roughness element on the turbulent velocity field was determined by measuring vertical profiles of the vertical velocity component in the region downstream of the basal obstruction with the Ultrasonic Doppler Velocity Profiling technique. The experiments were set up to answer two research questions. (i) How does a single roughness element alter the distribution of vertical turbulence intensity? (ii) How does the altered profile evolve in the downstream direction? The results for runs over a plane substrate are similar to data presented previously and show a lower turbulence maximum near the channel floor, a turbulence minimum associated with the velocity maximum, and a turbulence maximum associated with the upper flow interface. In the runs in which the flows were perturbed by the single roughness element, the intensity of the lower turbulence maximum was increased between 41% to 81%. This excess turbulence dissipated upwards in the flow while it travelled further downstream, but was still observable at the most distal measurement location (at a distance ca 39 times the roughness height downstream of the element). All results point towards a similarity between the near bed turbulence structure of turbidity currents and free surface shear flows that has been proposed by previous authors, and this proposition is supported further by the apparent success of a shear velocity estimation method that is based on this similarity. Theory of turbulent dispersal of suspended sediment is used to discuss how the observed turbulent effects of a single large roughness element may impact on the suspended sediment distribution in real world turbidity currents. It is concluded that this impact may consist of a non‐equilibrium net‐upwards transport of suspended sediment, counteracting density stratification. Thus, erosive substrate topography created by frontal parts of natural turbidity flows may super‐elevate sediment concentrations in upper regions above equilibrium values in following flow stages, delay depletion of the flow via sedimentation and increase their run‐out distance.     

Deposit architecture and dynamics of the 2006 block‐and‐ash flows of Merapi Volcano,Java, Indonesia

The internal architecture of the 2006 block‐and‐ash flow deposits of Merapi volcano (Java, Indonesia) was investigated using data collected from 27 stratigraphic sections measured immediately after flow emplacement, and after one and two rainy seasons of erosion. Identification of different depositional units and their longitudinal and lateral facies variations provide detailed information about: (i) the distribution, volumes and sedimentological characteristics of the different units; (ii) flow types and mobility as inferred from associated deposits; and (iii) changes in the dynamics of the different flows and their material during emplacement. Two main types of block‐and‐ash flows (short‐runout to medium‐runout block‐and‐ash flows and long‐runout block‐and‐ash flows) are defined based on flow generation mechanism, flow volume, travel distance, deposit morphology, distribution, lithology and grain‐size distribution. Conceptual models for the transport and depositional mechanisms of these two types of block‐and‐ash flows are presented. Variations in the runout distances observed for short‐runout to medium‐runout block‐and‐ash flows are linked directly to different initial flow volumes, degree of fragmentation and material properties of the moving mass during transport, with the largest and finer grained flows having the greatest mobility. Deposition occurs only over a narrow range of basal inclinations close to the angle of repose for pyroclastic material, indicating that such flows behave in a similar way to granular‐free surface flows on unconfined planes. The flow mechanisms of long‐runout block‐and‐ash flows at Merapi are interpreted to be similar, in many respects, to unsteady, cohesionless grain flows with an inertial flow regime where collisional forces largely overcome frictional forces. Flow unsteadiness causes the main body to be segmented into different pulses that run closer to each other as the flow moves downslope. Deposition occurs stepwise, with rapid aggradation of stacked sub‐units from different parts of the major flow pulses. In such a model, the arrival of each flow pulse front at selected sites in the main river valley controls the generation and development of highly mobile, unconfined pyroclastic flows outside valley regions and their associated overbank deposits.     

春末黄土高原半干旱区地表能量闭合的观测研究

利用兰州大学半干旱气候与环境监测站的连续观测数据,分析了该站的数据质量情况和黄土高原半干旱区的近地层湍流通量特征及地表能量平衡能量闭合状况.结果表明:兰州大学半干旱气候与环境监测站(SACOL)湍流通量的平均时间取30min为宜.该站利用EdiRe获得的湍流通量较TK2和CR5000数据自动记录器输出的湍流通量结果要好.黄土高原半干旱区近地层湍流能量与地表含水量状况明显相关,地表干燥时感热通量处于主导地位,接近于干旱区的特征;地表湿润时感热通量和潜热通量则相当,接近于湿润地区的特征.地表能量平衡分析表明,兰州大学黄土高原半干旱环境监测站观测的地表能量闭合度高达85%,与已有的观测相比,能量闭合情况属于较好水平.     

基于多松弛格子玻尔兹曼的弯道水流三维数值模拟

为研究弯道水流现象并且拓展格子玻尔兹曼(Lattice Boltzmann Method,LBM)在水利工程领域的应用,建立了弯道水流的三维多松弛LBM演进模型,其中包括水流自由表面模拟、弯曲固壁边界处理以及紊流模型耦合求解等关键技术。应用该模型模拟研究了不同流量下U型弯道的水流状态,得到了水位、最大水深平均流速以及紊动能等参数的分布规律。分析和实践表明,该模型能较好地模拟三维弯道水流现象。     

Unified modelling of granular media with Smoothed Particle Hydrodynamics

In this paper, we present a unified numerical framework for granular modelling. A constitutive model capable of describing both quasi-static and dynamic behaviours of granular material is developed. Two types of particle interactions controlling the mechanical responses, frictional contact and collision, are considered by a hypoplastic model and a Bagnold-type rheology relation, respectively. The model makes no use of concepts like yield stress or flow initiation criterion. A smooth transition between the solid-like and fluid-like behaviour is achieved. The Smoothed Particle Hydrodynamics method is employed as the unified numerical tool for both solid and fluid regimes. The numerical model is validated by simulating element tests under both quasi-static and flowing conditions. We further proceed to study three boundary value problems, i.e. collapse of a granular pile on a flat plane, and granular flows on an inclined plane and in a rotating drum.     

Downstream lightening and upward heavying: Experiments with sediments differing in density

Sorting and selective transport of particles by material density is important for understanding a wide range of processes, including the formation of mineral placers, deposition of mine tailings and routing of tracers and contaminants. This article describes an experimental study of the transport of mixtures of particles of differing density in a sediment‐feed flume. During the runs, a downstream prograding wedge‐shaped deposit was formed. Results show two sorting processes: (i) longitudinal sorting characterized by preferential deposition of heavy particles in the upstream part of the deposit – downstream lightening; and (ii) vertical sorting with less dense particles preferentially deposited in the lowermost portion of the migrating front – upward heavying. Downstream lightening is the analogue of the well‐known downstream fining observed in the more studied case of mixtures of heterogeneous size with the same density. In both cases, the lighter particles are carried further downstream than the heavier particles. Upward heavying is unexpected when compared with deposits of heterogeneous size and same‐density particles, where the heaviest (i.e. coarsest) particles are deposited in the lowermost part of the front. The physical mechanism underlying this upward heavying might be related to the physics of gravity‐driven granular flows; the front of the deposit acts like a dense granular flow down an inclined plane. In this case, the denser particles settle away from the free surface and at the top of the heap, while the lighter particles flow to the bottom. As the front of the deposit advances, this progressively gives rise to an upward heavying pattern. The application of classical surface‐based fractional bedload transport models suggests that equal mobility is not approached in the case of mixtures of particles with uniform size and different densities. This study hypothesizes that other mechanics related to the physics of the segregation processes in these systems contribute to these results.     

Modelling and numerical simulation of two-phase debris flows

Gravity-driven geophysical mass flows often consist of fluid–sediment mixtures. The contemporary presence of a fluid and a granular phase determines a complicated fluid-like and solid-like behaviour. The present paper adopts the mixture theory to incorporate the two phases and describe their respective movements. For the granular phase, a Mohr–Coulomb plasticity is employed to describe the relationship between normal and shear stresses, while for the fluid phase, the viscous Newtonian fluid is taken into account. At the basal topography, a Coulomb sliding condition for the solid phase and a Navier’s sliding condition for the fluid phase are satisfied, while the top free surface is traction-free for both the phases. For the interactive forces between the phases, the buoyancy force and viscous drag force are included. The established governing equations are expressed in a curvilinear coordinate system embedded in a curvilinear reference basal surface, above which an arbitrary shallow basal topography is permitted. Taking into account the typical length characteristics of such geophysical mass flows, the “thin-layer” approximation is assumed, so that a depth integration can be performed to simplify the governing equations. The resulting strongly nonlinear partial differential equations (PDEs) are first simplified and then analysed for a steady state in a travelling coordinate system. We find the current model can reproduce the characteristic shape of some flow fronts. Additionally, a stability analysis for steady uniform flows is performed to demonstrate the development of roll waves that means instabilities grow up and become clearly distinguishable waves. Furthermore, we numerically solve the resulting PDEs to investigate general unsteady flows down a curved surface by means of a high-resolution non-oscillatory central difference scheme with the total variation diminishing property. The dynamic behaviours of the granular and fluid phases, especially, the effects of the drag force and the fluid bed friction are discussed. These investigations can enhance the understanding of physics behind natural debris flows.     

Rock-avalanche dynamics: insights from granular physics experiments

Rock avalanches are known to behave in extraordinary ways unlike other landslides, and their deposits in part reflect their unusual physical behavior. Recent experiments in granular physics suggest that many phenomena and features simply reflect the non-linear nature of granular flows, although some behavior cannot simply be reproduced in lab scale experiments. In a static configuration, grain–grain contact networks dominate the distribution of forces and stresses within a granular mass. During flow, granular collisions damp the system through energy dissipation, while gravitational potential drives the system. The energy distribution between static and collisional stresses within the system can change very rapidly. Threshold events dominate system response, and the challenge is to find which characterization of the static phase helps to predict failure (and thus flow) resistance. Once flowing, many “unusual” rock-avalanche phenomena are entirely consistent with the physics of flow of large granular masses, but the low energy dissipation rate required for long run-out events requires the presence of physical processes that are not involved in experimental flows in the current parameter range or in the assumptions of current models.     

二维粒状材料双轴压缩试验研究

为了研究粒状材料的各向异性力学行为与细观组构演化之间的关系,采用自主研发的双轴压缩试验系统,以圆形和椭圆形截面的金属棒状材料组成的二维堆积体为试验对象,对不同大主应力方向角?（沉积面与大主应力作用面的夹角）的试样进行了各向等压、常侧向压力、等p剪切3种应力路径试验,并通过分析试样在不同变形阶段的数字照片得到了其细观组构演化规律。发现对于椭圆形截面的试样存在一个卓越剪切方向,随剪应变增大,颗粒长轴呈现出向该方向偏转的趋势,并且在大变形条件下沿该方向形成剪切带;卓越剪切方向与沉积面方向关系不大,而与大主应力作用面方向夹角约为45°+ /2, 为残余内摩擦角;随卓越剪切方向与沉降方向夹角的不同,颗粒偏转程度的不同是导致剪胀特性和峰值强度各向异性的主要原因     

几种紊流模型在底坎紊流分离流计算中的对比

利用标准模型κ-ε、重整群κ-ε模型和v2f三种不同的紊流模型,在同位网格系统基础上,采用了有限控制体积离散方程,数值模拟了底坎所形成紊流分离流。计算结果表明,所选用的3种模型虽大致都能模拟出底坎分离流的流动特性,如前后角涡、回流型态等,但在主涡心位置、回流长度、水头损失和流速分布等方面3种模型计算结果有所差异,其中v2f模型所计算的结果同试验和大涡模拟的结果值更趋一致。结果表明,v2f模型具有更精确模拟底坎所形成的紊流分离流方面的优势。     

用VOF方法模拟静止浅水环境中的垂向紊动射流

以k-ε紊流模型为基础,针对浅水环境垂向射流的水面会有明显突起情况,采用VOF(Volume of Fluid)方法追踪自由面,建立了适合浅水环境垂向平面紊动射流的二维数学模型.对不同入射速度、水深、入射口宽度组合进行了大量的数值模拟实验,对整个流场的分布作了分析,发现自由面的分布特点和速度矢量场的分布特点相对应;中轴线附近的自由面隆起具有自相似性,文中给出了拟合表达式;由于水面的阻滞,中轴线上垂向速度的衰减较自由射流快,衰减规律随水深和射流宽度而异.     

Predictability of long runout landslide motion: implications from granular flow mechanics

Quality of landslide motion prediction is directly linked to the understanding of the basic flow mechanisms. Although it is known that landslides are granular mass flows and granular flow mechanics is an established area of research, hypotheses on landslide motion are still based on simple geometrical relations and heuristic assumptions. New insights into the development of flow properties of high-speed, high-concentration granular flows are given by results of discrete particle simulations: rapid granular flows are self-organizing dynamic systems that are forced to develop a plastic body rheology. This behaviour must be described by a coefficient of internal friction μ_CM that refers to the center of mass of a flow. Coefficients of rapid granular flows of inelastic and rough particles, which are typical for common rock materials, do not vary significantly around μ _CM ≈0.45 that is definitively smaller than the friction coefficient of soil creep (≈0.6). The motion of the center of mass is superimposed by the spreading of the granular mass that is controlled by the same plastic body rheology. This combined motion is a scale-invariant self-similar process that depends only on the drop height of a landslide and its volume. This allows specification of implications that must be given special attention in the development of future models for landslide prediction.