A conceptual, continuous time model called SWAT (Soil and Water Assessment Tool) was developed to assist water resource managers in assessing the impact of management on water supplies and nonpoint source pollution in watersheds and large river basins. The model is currently being utilized in several large area projects by EPA, NOAA, NRCS and others to estimate the off-site impacts of climate and management on water use, nonpoint source loadings, and pesticide contamination. Model development, operation, limitations, and assumptions are discussed and components of the model are described. In Part II, a GIS input/output interface is presented along with model validation on three basins within the Upper Trinity basin in Texas.

Large Area Hydrologic Modeling and Assessment Part i: Model Development

Grain size analysis is an essential tool for classifying sedimentary environments. The calculation of statistics for many samples can, however, be a laborious process. A computer program called GRADISTAT has been written for the rapid analysis of grain size statistics from any of the standard measuring techniques, such as sieving and laser granulometry. Mean, mode, sorting, skewness and other statistics are calculated arithmetically and geometrically (in metric units) and logarithmically (in phi units) using moment and Folk and Ward graphical methods. Method comparison has allowed Folk and Ward descriptive terms to be assigned to moments statistics. Results indicate that Folk and Ward measures, expressed in metric units, appear to provide the most robust basis for routine comparisons of compositionally variable sediments. The program runs within the Microsoft Excel spreadsheet package and is extremely versatile, accepting standard and non-standard size data, and producing a range of graphical outputs including frequency and ternary plots. Copyright © 2001 John Wiley & Sons, Ltd.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/esp.261

GRADISTAT: a grain size distribution and statistics package for the analysis of unconsolidated sediments

The Intergovernmental Panel on Climate Change (IPCC) Technical Paper Climate Change and Water draws together and evaluates the information in IPCC Assessment and Special Reports concerning the impacts of climate change on hydrological processes and regimes, and on freshwater resources – their availability, quality, use and management. It takes into account current and projected regional key vulnerabilities, prospects for adaptation, and the relationships between climate change mitigation and water. Its objectives are:

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Climate change and water.

The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0BD9AC7975884A5D5F360188D647F2B6/S0022112084000586a.pdf/div-class-title-kinetic-theories-for-granular-flow-inelastic-particles-in-couette-flow-and-slightly-inelastic-particles-in-a-general-flowfield-div.pdf

Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield

Recent advances in theory and experimen- tation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid-fluid mixtures provide a foundation for a com- prehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoret- ical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining stat- ic; both can deform in a slow, tranquil mode character- ized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompress- ible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (mea- sured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibra- tional energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of ;10 m 3 of poorly sorted, water-saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse-grained surge fronts have little or no pore fluid pressure. In contrast, finer-grained, thoroughly saturated debris be- hind surge fronts is nearly liquefied by high pore pres- sure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic mod- els of debris flows therefore require equations that sim- ulate inertial motion of surges in which high-resistance fronts dominated by solid forces impede the motion of low-resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristi- cally originate as nearly rigid sediment masses, trans- form at least partly to liquefied flows, and then trans- form again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth-averaged equations of motion patterned after those of the Savage-Hutter theory for gravity-driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behav- iors intermediate between those of wet rock avalanches and sediment-laden water floods. With appropriate pore pressure distributions the equations yield numerical so- lutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

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The physics of debris flows

The physics of blown sand and desert dunes , The physics of blown sand and desert dunes , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

The Physics of Blown Sand and Desert Dunes

Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. Both the stresses T and P , as dimensionless groups T σ D 2 /λη 2 , and P σ D 2 /λη 2 , were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½ σ D 2 (d U /d y )lη for all the values of λ C = 57% approx.) where d U /d y is the rate of shearing of the grains over one another, and η the fluid viscosity. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U /d y is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U /d y was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.

Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear

/pdf/an-approach-to-the-sediment-transport-problem-from-general-55s8d8ax7z.pdf

An approach to the sediment transport problem from general physics

Part I . The results of previous experiments (Bagnold 1954) on the stresses set up in a uniform gravity-free dispersion of solid grains when uniformly sheared in a fluid are applied to the nonuniform case of grain flow over a gravity bed, assuming the results are quantitatively applicable to any sufficiently thin shear layer. It is found that if the bed is composed entirely of potentially mobile grains a stress-equilibrium relation at the bed surface can be defined whereby the magnitude of a certain ‘bed load’ of grains in transit over unit bed area is given in terms of the applied tangential stress. The bed load is independent both of the existence of any additional suspended load and of the degree of dispersion of the grains. The state of internal fluid motion enters as a single experimental constant. From a consideration of the stability of this equilibrium relation it is possible to predict the conditions under which an initially plane bed surface should become rippled; and general quantitative agreement is found with experimental data both for wind-blown and water-driven grains. Primary and secondary bed rippling are distinguished. The magnitude of the ‘form-drag’ due to primary bed ripples can be calculated. That due to secondary ripples is definable as an experimental constant. The gravity-free experiments disclosed that the shear resistance of a grain dispersion may vary as the square or the first power of the rate of shear, analogously to that of a true fluid, according to the value of a number G analogous to a Reynolds number. The square law is followed when the effects of grain inertia dominate over those of fluid viscosity. Assuming that the phenomenon of ‘saltation’ as observed over a gravity bed is an inertia effect, the conditions for saltation are predictable. The results again agree quantitatively with observation. Part II . The resistance offered by the grains to their displacement along the flow is shown to be proportional to their normal immersed weight component. And their measurable mass transport rate is hereby proportional to the rate of useful work done in transporting them. On this basis separate expressions are found for the transport rates of the bed load and suspended load, in terms of the applied tangential stress and of a tangential and a normal relative velocity respectively. When conditions are restricted to those of the ‘stream case’ these velocities become constant for any given system, being functions of an appropriate constant mean drag coefficient. The bed-load transport-rate expression found gives magnitudes, and variations of magnitude with grain size, in agreement with the experimental data for wind-blown sand. Agreement is also found for water-driven grains in open channels from the threshold of movement up to a certain value of the applied stress. The experimental rates are then found to increase suddenly. This increase is attributed to the development of an additional suspended load. The abrupt development of a suspended load may be explained as due to a change in the nature of the fluid turbulence when the stationary boundary becomes occluded from the fluid flow by a concentrated layer of moving bed-load grains. The assumption that under these new moving-boundary conditions the available fluid energy derived from shearing over the bed is equally apportioned between bed-load and suspended-load transport work leads to values for the suspended-load transport rate which agree closely with the experimental data. A critical relation emerges between the gravity slope of the bed, the fall velocity and the mean transport velocity of the suspended grains at which their transport may become very large. Conditions are examined under which the steady transport may be possible of grains of heterogeneous size or density. Part III . When the fluid flow is non-inertial (laminar) and the grain flow is also non-inertial the semi-empirical relations found previously for the internal stresses are such that both viscosity and shear rate can be eliminated, and a differential equation obtained whose solution gives the grain concentration in terms only of distance from the bed and of the applied tangential stress. It appears that with constant applied stress (unlimited flow depth) the degree of grain dispersion greatly exceeds that to be expected in turbulent fluid flow. But when the applied stress diminishes linearly with distance from the bed boundary a possible solution gives constant grain concentration throughout the flow. This appears to explain certain experimental results, including the behaviour of ‘slurries’. The effect is examined of a fixed or partially fixed bed on the grain flow in a turbulent fluid. The effect may be pronounced in the case of suspended grains. Under certain clearly definable conditions a loose grain bed must cease to remain stationary. And if the fluid flow above is turbulent the whole grain bed should flow at constant maximum concentration, underneath the flow proper and separated from it by a moving-bed surface interface at which the concentration is discontinuous. This explains phenomena sometimes found under river torrents. The factors giving rise to and limiting the development of bed features (dunes) on a bigger scale than ripples are examined. Dune formation appears as an inherent tendency of the grain flow alone, which may or may not be inhibited by the conditions of the fluid flow.

The flow of cohesionless grains in fluids

Since stream power ω and sediment transport rate i are different values of the same physical quantity, namely, the time rate of energy supply and dissipation, it is rational to relate one to the other. The experimental relation has been difficult to interpret because of the spurious curvature of log-log plots in which a constant threshold stream power of zero is involved. The substitution of an excess power ω − ω0 removes this curvature, and existing data on laboratory bed load transport rate measurements ib suggest a general empirical relation: ib ∝ (ω − ω0)[(ω − ω0);0]½. Existing laboratory data have also shown clearly that at any given value of ω − ω0 the bedload transport rate ib decreases as an inverse function of the ratio flow depth to grain size Y/D. The East Fork River (Wyoming) project has recently enabled bed load sampling devices to be calibrated, so reasonably reliable measurements can be made in natural rivers. The uncertainties in the measurement of the corresponding river power are discussed, and a simple data reliability test is suggested. Data covering three seasons collected from both Snake and Clearwater rivers appear to be reliable. Though there is much scatter due to day variations in the river conditions, these data, together with data on an imtermediate scale from East Fork River and on a small laboratory scale, conform with startling consistency to the following general empirical relation: ib/(ω − ω0) ≈ [(ω − ω0)/ω0]½(Y/D)−⅔ over a 2 million-fold range of stream discharge. The degree of consistency of the above empirical relation with the theoretical relation deduced previously (Bagnold, 1973) is discussed, as are also some morphological implications of the dependence of ib on the depth to grain size ratio Y/D.

R. A. Bagnold

Papers

The Physics of Blown Sand and Desert Dunes

Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear

An approach to the sediment transport problem from general physics

The flow of cohesionless grains in fluids

Bed load transport by natural rivers