Hydrodynamic characteristics of rill flow on steep slopes

Rill erosion is a dominant sediment source on sloping lands. However, the amount of soil loss from rills on steep slopes is vastly more than that on gentle slopes because of differences in rill shape and hydraulic patterns. The aims of this paper are to determine the hydrodynamic characteristics of rills and the friction coefficients in steep slope conditions and to propose modifications of some hydraulic parameters used in soil loss prediction models. A series of inflow experiments was conducted on loess slopes. The results show that the geometric and hydraulic properties of rill on the steep loess slopes, which are characterized by the mean width of cross sections, mean velocity and mean depth of flow, are related to discharge and slope gradient in power functions. However, the related exponents to discharge are 0.26, 0.48 and 0.26, respectively, which are different from the exponents derived in previous studies, which were conducted on gentle slopes. The Manning roughness coefficient ranged from 0.035 to 0.071, with an average of 0.0536, and the Darcy–Weisbach friction coefficients varied from 0.4 to 1.9. The roughness coefficients are closely related to the Reynolds numbers and flow volumes; however, the correlations vary with slope gradient. The roughness coefficients are directly proportional to the Reynolds number and the flow volume on steep slopes, in contrast with the roughness coefficients found on gentle slopes, which decrease as the Reynolds number and flow volume increase. This difference is caused by the interactions among the hydraulics of the flow, the shape of the rills and the sediment concentrations on steep slopes. The results indicate that parameters used in models to predict rill erosion have to be modified according to slope gradient. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental Investigation of Kinetic Energy and Momentum Coefficients in Regular Channels with Stiff and Flexible Elements Simulating Submerged Vegetation

The paper addresses the problem of determination of the energy and momentum coefficients for flows through a partly vegetated channel. These coefficients are applied to express the fluid kinetic energy and momentum equations as functions of a mean velocity. The study is based on laboratory measurements of water velocity distributions in a straight rectangular flume with stiff and flexible stems and plastic imitations of the Canadian waterweed. The coefficients were established for the vegetation layer, surface layer and the whole flow area. The results indicate that the energy and momentum coefficients increase significantly with water depth and the number of stems per unit channel area. New regression relationships for both coefficients are given.     

Modeling high-order statistics in the turbulent Ekman layer

Results from a direct numerical simulation (DNS) of the neutral and unstable turbulent Ekman layer at a Reynolds number of 1000 were used to evaluate turbulence closure models. For the neutrally stratified Ekman layer, the higher-order moments of velocity were examined and the accuracy of a kurtosis model was assessed. For the unstable Ekman layer, the analysis of higher-order moments was extended to temperature-velocity correlations. Model coefficients were optimised using DNS data and it was shown that the optimised models accurately captured the distributions of all fourth-order moments. These low-Reynolds number results can be extrapolated to higher Reynolds numbers to parameterise turbulence in other flow fields with rotational effects such as the atmospheric boundary layer.     

Predicting wetted width in any river at any discharge

Coefficients describing at‐a‐station power‐law relationships between discharge and width were calculated by applying multilevel models to field data collected during routine hydrological monitoring at 326 gauging stations across New Zealand. These hydraulic geometry coefficients were then estimated for each of these stations using standard stepwise multiple‐linear regression models. Analysis was carried out to quantify how the relationship between width and discharge changed in relation to several available explanatory variables. All coefficients describing the at‐a‐station hydraulic geometry were found to have statistically significant relationships with catchment area. Statistically significant relationships between each of the coefficients were also found with the addition of catchment climate as an explanatory variable. Further statistically significant relationships were found when station elevation and channel slope, as well as hydrological source of flow and landcover of the upstream catchment were added to the explanatory variables. The level of confidence that can be associated with estimates of width at ungauged sites, and sites with limited data availability, was then assessed by comparing model predictions with independent paired data on observed width and discharge from 197 sites. When compared against these independent data, model predictions of width were improved with the addition of predictor variables of the hydraulic geometry coefficients. The greatest improvements were made when climate was added to catchment area as predictor variables. Minor improvements were made when all available information was used to predict width at these independent sites. Although the analysis was purely empirical, results describing relationships between hydraulic geometry coefficients and catchment characteristics corresponded well with knowledge of the processes controlling at‐a‐station hydraulic geometry of river width. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady hydromagnetic flow in a porous annulus with time-dependent pressure gradient

Summary Problem of unsteady motion of a conducting viscous incompressible fluid through an annulus with porous walls under an external radial magnetic field has been discussed. Taking the Reynolds number and the magnetic Reynolds number to be equal, exact solution of the problem is obtained in terms of Bessel functions when the motion is due to the time-dependent pressure gradient or the time-dependent velocity of either of the boundaries. Two types of dependence on time are considered; one, exponentially increasing, and the other, exponentially decreasing. Solutions in certain extreme cases are also discussed.     

Nonlinear radial oscillations of coronal loops

The behavior of radial oscillations of coronal magnetic tubes is considered in a weakly nonlinear approximation. The nonlinear Schrödinger equation, the coefficients of which are found from the tube and radial mode parameters, has been obtained for the oscillation amplitude. The coefficients have been calculated for the fundamental radial mode, which is characterized by the absence of the cutoff in the region of low frequencies. It has been shown that the modulation instability condition is satisfied in a wide range of mode parameter values, which indicates that large-amplitude radial oscillations can exist in coronal loops.     

水平单轴应力与横波反射系数

地球物理勘探中,地下应力的估测是非常重要的.本文利用应力诱导的弱各向异性的各向异性参数,借助已有的具有水平对称轴横向各向同性介质顾及高阶小量的横波反射系数近似公式,针对下介质为各向同性受单轴应力作用情况随应力的增加求取应力精度降低的问题,从横波反射系数近似公式的推导出发,联合SH波与SV波反射系数给出新的改进的单轴应力与横波反射系数的直观表达式;计算并对比了受单轴应力作用的各向同性介质的横波近似和严格的反射系数,并利用理论得到的横波反射系数对应力进行了估值.结果表明,利用改进后横波反射系数与应力的直观表达式,当应力增加时,应力估值精度有了明显的改善,这为利用横波反射数据直观估测应力提供理论依据.     

Experimental investigation of drag coefficients of gobi surfaces

The response of gobi surfaces to the near-surface air flow can be characterized quantitatively by drag coefficients. By using wind tunnel tests, an attempt is made to define the relationship between the drag coefficients of gobi surfaces and gravel size and coverage. It is concluded that the drag coefficients of gobi surfaces tend to be constants when gravel coverage is over 40%-50%. Consequently, we think that the gobi deflation planes expanding vastly in the arid Northwestern China are aerodynamically stable, at least not the supplying sources of current dust storms, and therefore the emphasis on dust storm control should be paid on the so-called "earth gobi" that has low gravel coverage. The prediction model for drag coefficients of gobi surfaces has been developed by regressing drag coefficients on gravel size and coverage, the predicted results are in reasonably good agreement with wind tunnel results (R 2 = 0.94). The change of drag coefficients with gravel friction Reynolds number implies that the development extent of drag effect increases with gravel size and coverage.     

Exact analytical solutions for two-dimensional advection-dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition

Exact analytical solutions for two-dimensional advection-dispersion equation (ADE) in cylindrical coordinates subject to the third-type inlet boundary condition are presented in this study. The finite Hankel transform technique in combination with the Laplace transform method is adopted to solve the two-dimensional ADE in cylindrical coordinates. Solutions are derived for both continuous input and instantaneous slug input. The developed analytical solutions are compared with the solutions for first-type inlet boundary condition to illustrate the influence of the inlet condition on the two-dimensional solute transport in a porous medium system with a radial geometry. Results show significant discrepancies between the breakthrough curves obtained from analytical solutions for the first-type and third-type inlet boundary conditions for large longitudinal dispersion coefficients. The developed solutions conserve the solute mass and are efficient tools for simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment or an in situ infiltration test with a tracer.     

Modeling River Stage‐Discharge Relationships Using Different Neural Network Computing Techniques

One of the most important problems in hydrology is the establishment of rating curves. The statistical tools that are commonly used for river stage‐discharge relationships are regression and curve fitting. However, these techniques are not adequate in view of the complexity of the problems involved. Three different neural network techniques, i. e., multi‐layer perceptron neural network with Levenberg‐Marquardt and quasi‐Newton algorithms and radial basis neural networks, are used for the development of river stage‐discharge relationships by constructing nonlinear relationships between stage and discharge. Daily stage and flow data from three stations, Yamula, Tuzkoy and Sogutluhan, on the Kizilirmak River in Turkey were used. Regression techniques are also applied to the same data. Different input combinations including the previous stages and discharges are used. The models' results are compared using three criteria, i. e., root mean square errors, mean absolute error and the determination coefficient. The results of the comparison reveal that the neural network techniques are much more suitable for setting up stage‐discharge relationships than the regression techniques. Among the neural network methods, the radial basis neural network is found to be slightly better than the others.     

Determination of Forchheimer equation coefficients a and b

This study focuses on the determination of the Forchheimer equation coefficients a and b for non‐Darcian flow in porous media. Original theoretical equations are evaluated and empirical relations are proposed based on an investigation of available data in the literature. The validity of these equations is checked using existing experimental data, and their accuracy versus existing approaches is studied. On the basis of this analysis, some insight into the physical background of the phenomenon is also provided. The dependence of the coefficients a and b on the Reynolds number is also detected, and potential future research areas, e.g. investigation of inertial effects for consolidated porous media, are pointed out. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling preasymptotic transport in flows with significant inertial and trapping effects – The importance of velocity correlations and a spatial Markov model

We study solute transport in a periodic channel with a sinusoidal wavy boundary when inertial flow effects are sufficiently large to be important, but do not give rise to turbulence. This configuration and setup are known to result in large recirculation zones that can act as traps for solutes; these traps can significantly affect dispersion of the solute as it moves through the domain. Previous studies have considered the effect of inertia on asymptotic dispersion in such geometries. Here we develop an effective spatial Markov model that aims to describe transport all the way from preasymptotic to asymptotic times. In particular we demonstrate that correlation effects must be included in such an effective model when Péclet numbers are larger than O(100) in order to reliably predict observed breakthrough curves and the temporal evolution of second centered moments. For smaller Péclet numbers correlation effects, while present, are weak and do not appear to play a significant role. For many systems of practical interest, if Reynolds numbers are large, it may be typical that Péclet numbers are large also given that Schmidt numbers for typical fluids and solutes can vary between 1 and 500. This suggests that when Reynolds numbers are large, any effective theories of transport should incorporate correlation as part of the upscaling procedure, which many conventional approaches currently do not do. We define a novel parameter to quantify the importance of this correlation. Next, using the theory of CTRWs we explain a to date unexplained phenomenon of why dispersion coefficients for a fixed Péclet number increase with increasing Reynolds number, but saturate above a certain value. Finally we also demonstrate that effective preasymptotic models that do not adequately account for velocity correlations will also not predict asymptotic dispersion coefficients correctly.     

震级与地震破裂参数统计关系式系数的讨论

在收集６种类型震级与地震破裂参量的统计关系式的基础上，系统分析和总结了各类统计式的系数ａｉ和ｂｉ的变化范围以及二者的关系。发现ａｉ和ｂｉ之间均有或强或弱的负相关性；不同类型统计式的系数有一定的变化范围，且稳定性和收敛度不同。一般来说，涉及的破裂参量越多系数越稳定。最后依据位错公式，解释了ａｉ和ｂｉ的关系     

A short-term predictive system for surface currents from a rapidly deployed coastal HF radar network

In order to address the need for surface trajectory forecasts following deployment of coastal HF radar systems during emergency-response situations (e.g., search and rescue, oil spill), a short-term predictive system (STPS) based on only a few hours data background is presented. First, open-modal analysis (OMA) coefficients are fitted to 1-D surface currents from all available radar stations at each time interval. OMA has the effect of applying a spatial low-pass filter to the data, fills gaps, and can extend coverage to areas where radial vectors are available from a single radar only. Then, a set of temporal modes is fitted to the time series of OMA coefficients, typically over a short 12-h trailing period. These modes include tidal and inertial harmonics, as well as constant and linear trends. This temporal model is the STPS basis for producing up to a 12-h current vector forecast from which a trajectory forecast can be derived. We show results of this method applied to data gathered during the September 2010 rapid-response demonstration in northern Norway. Forecasted coefficients, currents, and trajectories are compared with the same measured quantities, and statistics of skill are assessed employing 16 24-h data sets. Forecasted and measured kinetic variances of the OMA coefficients typically agreed to within 10–15%. In one case where errors were larger, strong wind changes are suspected and examined as the cause. Sudden wind variability is not included properly within the STPS attack we presently employ and will be a subject for future improvement.     

长江中游夏季降水场预报技术研究

经SVD分析,截取足够多的预报场和因子场时间系数,使其相互关系代表两场的大尺度联系,预报场时间系数与其奇异向量线性组合估计场能反映原场主要特征.借助最优化技术,选择合理的系数,建立预测公式,由因子场时间系数预测预报场时间系数,同时订正预报场时间系数心a₁ a₂ a_N本身的误差和反演过程中分析误差造成的场格点趋势预测的误差.最后将预测的预报场时间系数和对应奇异向量反演为整个场的预报.预报过程重点考虑可预报的大尺度变化,滤去不可预报的小扰动,依据两场主要耦合关系,预测预报场未来的主要变化.     

Heat transfer coefficients of natural volcanic clasts

Heat transfer coefficients used in numerical simulations of volcanic eruptions are typically borrowed from industrial settings where the coefficients are well determined for non-permeable, machined (spherical) materials. Volcanic clasts, in contrast, are permeable and have irregular shapes. We performed a series of laboratory experiments to determine heat transfer coefficients for natural volcanic particles. We measured the surface and interior temperatures during cooling at wind speeds ranging from 0 to 10 m/s. We also measured the permeability and density of the particles. We find that the permeability of the particles has little effect on clast cooling. In the absence of any wind, heat loss occurs by free convection, and we find no relationship between the heat transfer coefficient and particle density. However, for non-zero Reynolds numbers (finite wind speed), the heat transfer coefficient decreases with increasing porosity. We obtain a correlation for the dimensionless heat loss, or Nusselt number, of the form Nu = 2 + aRe^1/2Pr^1/3 where a is a density dependent coefficient given by a = 0.00022ρ + 0.31, with ρ in kg/m³, and Re and Pr are the Reynolds number and Prandtl number, respectively. Compared with non-porous particles, heat transfer coefficients for natural pumice clasts are reduced by a factor of 2–3 for particles with similar Re. Numerical simulations show that this leads to an increase in depositional temperature by 50–90 °C.     

Relationships between three dispersion measures used in flood frequency analysis

Three dispersion measures of a random variable, i.e., the standard deviation, the mean deviation (MD) about the mean and the second L-moment, are analyzed in terms of their properties and mutual relationships. Emphasis is placed on the MD, as it is less recognized than two other dispersion measures. The relationships between the dispersion measures are derived for distributions commonly applied in flood frequency analysis (FFA). For distributions that are unbounded, there is a distribution-dependent constant value of the ratio of dispersion measures, or equivalently of respective coefficients of variation. For two-parameter distributions that are lower-bounded, the relationship between the coefficients of variation is also distribution dependent and is not linear. For lower-bounded three-parameter distributions, the dispersion measure ratios, or equivalently the ratios of coefficients of variation, depend on the coefficient of skewness and show a strong distributional dependence. For selected distributions, the three dispersion measures are compared both in terms of the robustness to the largest samples element and the accuracy of upper quantile estimation. The MD statistics may be highly competitive to the two other dispersion measure statistics if applied in FFA for parameters estimation.     

湍流输送的非线性热力学性质

湍流输送是一种热力学不可逆过程,本文利用非线性热力学研究了湍流输送的特征. 将热力学流对热力学力以平衡态作为参考态进行Taylor展开,可以得到湍流输送系数是系统宏观参量梯度的Taylor级数. 线性湍流输送系数是Reynolds湍流闭合方案的K闭合湍流输送系数;而湍流输送系数非线性项则是系统偏离热力学平衡态所造成的热力学非线性效应. 湍流输送系数这一热力学性质提供了一种热力学湍流闭合方案. 线性湍流输送系数是正定的,湍流输送只能使系统宏观参量均匀化;而在远离平衡态的热力学非线性区,可能导致湍流输送系数负黏性现象. 在最小熵产生态的条件下,热力学流对热力学力Taylor展开的各级系数间存在一种递推关系. 利用这种递推关系大大减少了由实验确定的Taylor级数的系数个数.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.