Hydraulic geometry and maximum flow efficiency as products of the principle of least action

Basic flow relationships have previously been seen to be insufficient to explain the self‐adjusting mechanism of alluvial channels and as a consequence extremal hypotheses have been incorporated into the analyses. In contrast, this study finds that by introducing a channel form factor (width/depth ratio), the self‐adjusting mechanism of alluvial channels can be illustrated directly with the basic flow relations of continuity, resistance and sediment transport. Natural channel flow is able to reach an optimum state (Maximum Flow Efficiency (MFE), defined as the maximum sediment transporting capacity per unit available stream power) with regard to the adjustment of channel form such that rivers exhibit regular hydraulic geometry relations at dominant or bankfull stage. Within the context of MFE, this study offers support for the use of the concepts of maximum sediment transporting capacity (MSTC) and minimum stream power (MSP). Furthermore, this study indicates that the principle of least action is able to provide a physical explanation for the existence of MFE, MSTC and MSP. Potential energy is minimized and consequently sediment transport is maximized in alluvial channels. Copyright © 2000 John Wiley & Sons, Ltd.     

Adjustment and recovery of unstable alluvial channels: Identification and approaches for engineering management

The management of riverine environments is shown to require a knowledge and awareness of the complex interactions between fluvial and mass-wasting processes, riparian vegetation, and channel form. Identification of the cause of instability rather than the local symptoms, and knowledge of the temporal and spatial aspects of channel adjustment are central to the application of (1) appropriate analyses to estimate future channel changes, (2) appropriate mitigation measures, and (3) the protection of river-crossing structures and adjacent land. Conceptual models of channel evolution and bank-slope development are particularly valuable for interpreting past and present processes, applying appropriate computational techniques to estimate future channel changes, and implementing strategies to mitigate the impacts of processes likely to dominate the channel in the future. Techniques for identification and analysis of channel instability are interdisciplinary and provide a mechanism for estimating changes in channel-bed elevation and channel width with time. Features of channel form and associated riparian vegetation can be used as diagnostic criteria to identify channel processes, the stage of channel evolution and the magnitude and extent of instability. Changes in bed elevation with time can be represented using an exponential function; changes in channel width with time can be calculated using slope stability equations and (or) projection of a temporary angle of stability from a low-angle surface termed the ‘slough line’ that supports re-establishment of woody vegetation. These techniques, in combination with knowledge of the state of channel evolution, can then be used to assess the appropriateness of various mitigation measures to control on-going channel adjustments and to protect river-crossing structures.     

Minimum froude number and the equilibrium of alluvial sand rivers

Rivers adjust towards an equilibrium condition, the stability of which depends upon a set of controlling factors expressed by the Froude number. As alluvial river channels approach stable conditions, the Froude number of the channel flow will tend to attain a minimum value which reflects minimum bed material motion and maximum channel stability, under the constraints imposed by water discharge, sediment load, and particle size. Computer simulations for sand bed rivers show that the Froude number of the flow tends to a minimum value when the equilibrium river tends to a certain hydraulic geometry. Evidence from 57 alluvial sand material rivers and stable canals shows that this simulated hydraulic geometry with minimum Froude number corresponds to the natural equilibrium state.     

Models of interacting pairs of thin,quasi-geostrophic vortices: steady-state solutions and nonlinear stability

We study pairwise interactions of elliptical quasi-geostrophic (QG) vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical “lenses” inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting non-elliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full QG dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N / f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions.     

A test of equilibrium theory and a demonstration of its practical application for predicting the morphodynamics of the Yangtze River

Taking the width/depth ratio of a river channel as an independent variable, a variational analysis of basic flow relationships shows that alluvial‐channel flow adjusts channel geometry to achieve stationary equilibrium when the condition of maximum flow efficiency (MFE) is satisfied. As a test of the veracity of MFE and to examine if this theory of self‐adjusting channel morphodynamics can be practically applied to large river systems, this study examines the degree of correspondence between theoretically determined equilibrium channel geometries and actual measurements along the middle and lower Yangtze River. Using four different forms of the Meyer‐Peter and Müller bedload relation and relations of flow continuity and resistance we show that the Meyer‐Peter and Müller bedload relation modified on the basis of MFE theory predicts channel dimensions most accurately when applied to the middle and lower Yangtze River. This provides convincing evidence supporting MFE equilibrium theory. Copyright © 2014 John Wiley & Sons, Ltd.     

The principle of discrete element method and its application in the study of regional tectonic stability

The basic principle of Discrete Element Method (DEM) is briefly introduced in this paper. Considering advantage of this method that using it the problems on discontinuous deformation of medium can be solved, we apply it to the study on movement of fault-blocks and activity of faults. The results indicate that the DEM has a good prospect in the analysis of regional tectonic stability. Using this method one can calculate the rotary movement of fault blocks, which will provide a new way to explain the stress concentration in some areas and the mechanism of earthquakes. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 456–462, 1992. This study is supported by National Natural Science Fund of China.     

Coupling action of rainfall and vehicle loads impact on the stability of loess slopes based on the iso-water content layer

To clarify the changes in slope stability of loess slopes under the coupling action of rainfall and vehicle loads. Experiments with different water contents under different environmental conditions were carried out indoors, and the relationship function between water content and shear strength parameters was obtained; Secondly, based on Geostudio, an equivalent layered calculation model of water content-strength parameters of loess slope was established, the variation law of soil sample matrix suction with volumetric water content was measured by volumetric pressure plate tester. Finally, by using a combination of finite element analysis of saturated/unsaturated seepage and limit equilibrium analysis of slope stability, the SLOPE/W module in the modeling software GeoStudio is used to calculate and analyze the effects of vehicle loads, rainfall intensity, rainfall duration, and other working conditions on the stability of loess slopes, respectively. The results show that when the lane is in the middle of the slope, the vehicle load parameters have little effect on the uphill stability, but have a greater impact on the downhill; With the increase in rainfall, the change curves of the slope safety coefficient gradually overlap when the vehicle loads are four-axis,five-axis, and six-axis. This shows that when studying the change of slope safety factor under the dual influence of vehicle loads and rainfall, rainfall is the main cause of slope stability; The change rate of slope safety factor increases gradually with the increase of rainfall, and the change trends of the upper, lower and overall parts of the slope are similar.     

Self‐adjustment in rivers: Evidence for least action as the primary control of alluvial‐channel form and process

Least action principle (LAP) in rivers is demonstrated by maximum flow efficiency (MFE) and is the foundation of variational mechanics based on energy and work rather than Newtonian force and momentum. Empirical evidence shows it to be the primary control for the adjustment of alluvial channels. Because most rivers flow with imposed water and sediment loads down valley gradients they have largely inherited, they self‐regulate energy expenditure to match the work they are required to do to remain stable. Overpowered systems develop a variety of channel patterns to expend excess energy and remain stable. Australia offers an opportunity to study low‐energy rivers closely adjusted to very low continental gradients. The anabranching Marshall and single‐thread Plenty Rivers flow down nearly straight channels with average H numbers [ratio between excess bed shear and width/depth (W/D) ratio] close to the optimum of 0.3 for stationary equilibrium. Ridge‐form divisions of the original channel width create anabranches that radically alter W/D ratios relative to bed shear, the same being true for short‐wide islands on the large low‐gradient Yangtze River in China. In contrast, Mount Chambers Creek in Australia's tectonically more active Flinders Ranges is accreting an alluvial fan with unstable distributary channels exhibiting H numbers well below the optimum. LAP also explains profound biases in Earth's stratigraphic record. Because meandering is an energy‐shedding mechanism, sinuous rivers sequester relatively little sediment resulting in all sequences being just a few tens of metres thick. In contrast, low‐energy braided disequilibrium systems can sequester sediment piles over a kilometre in thickness and tens of kilometres wide. LAP provides a new paradigm for river research by identifying the attractor state controlling river channel evolution. It links advances in theoretical physics to fluvial geomorphology, stratigraphy and hydraulic engineering and opens opportunities for diverse investigations in Earth system science. Copyright © 2016 John Wiley & Sons, Ltd.     

外界条件变化对天然气水合物相平衡曲线及稳定带厚度的影响

目前，有关天然气水合物的相关研究越来越多，而天然气水合物相平衡曲线和稳定带厚度的研究也变得越来越重要.本文利用Sloan的CSMHYD程序研究了外界条件变化对天然气水合物相平衡曲线及稳定带厚度的影响.研究结果表明：当天然气水合物中含有其他气体时，除了氮气会使水合物稳定存在的区域变小外；其他气体都会使稳定区域变大，且甲烷含量越少，水合物越容易形成；对于本文中所提到的几种气体，丙烷和硫化氢对相平衡曲线的影响最大；另外，水合物稳定存在的区域会随着盐度增加而变小.地温梯度、水深、海底温度、气体组成和孔隙水盐度对稳定带厚度的影响不同，其中稳定带厚度与地温梯度呈指数相关关系，与水深呈对数相关关系，与海底温度、水合物中甲烷含量及气体组成呈线性相关关系.水深从1 000 m增加到4 000 m时，稳定带厚度增加了大约400 m；水深2 000 m情况下，地温梯度从0.02℃/m到0.1℃/m变化时，稳定带厚度减薄了大约660 m；底水温度从0~17℃的变化过程中，稳定带厚度减薄了大约1000m；在水合物中气体组成从纯甲烷到含20%乙烷时，稳定带厚度增加了大约170m；盐度在0~4.5 wt％的变化中，稳定带厚度减薄了大约130 m.由此可见，在这几种因素中，地温梯度和底水温度对稳定带厚度的影响较大.