The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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.

/pdf/the-physics-of-debris-flows-1ncsxf8awr.pdf

The physics of debris flows

Since its first isolation in 2004, graphene has become one of the hottest topics in the field of materials science, and its highly appealing properties have led to a plethora of scientific papers. Among the many affected areas of materials science, this 'graphene fever' has influenced particularly the world of electrochemical energy-storage devices. Despite widespread enthusiasm, it is not yet clear whether graphene could really lead to progress in the field. Here we discuss the most recent applications of graphene - both as an active material and as an inactive component - from lithium-ion batteries and electrochemical capacitors to emerging technologies such as metal-air and magnesium-ion batteries. By critically analysing state-of-the-art technologies, we aim to address the benefits and issues of graphene-based materials, as well as outline the most promising results and applications so far.

The role of graphene for electrochemical energy storage

The complexity of flow and wide variety of depositional processes operating in subaqueous density flows, combined with post-depositional consolidation and soft-sediment deformation, often make it difficult to interpret the characteristics of the original flow from the sedimentary record. This has led to considerable confusion of nomenclature in the literature. This paper attempts to clarify this situation by presenting a simple classification of sedimentary density flows, based on physical flow properties and grain-support mechanisms, and briefly discusses the likely characteristics of the deposited sediments. Cohesive flows are commonly referred to as debris flows and mud flows and defined on the basis of sediment characteristics. The boundary between cohesive and non-cohesive density flows (frictional flows) is poorly constrained, but dimensionless numbers may be of use to define flow thresholds. Frictional flows include a continuous series from sediment slides to turbidity currents. Subdivision of these flows is made on the basis of the dominant particle-support mechanisms, which include matrix strength (in cohesive flows), buoyancy, pore pressure, grain-to-grain interaction (causing dispersive pressure), Reynolds stresses (turbulence) and bed support (particles moved on the stationary bed). The dominant particle-support mechanism depends upon flow conditions, particle concentration, grain-size distribution and particle type. In hyperconcentrated density flows, very high sediment concentrations (>25 volume%) make particle interactions of major importance. The difference between hyperconcentrated density flows and cohesive flows is that the former are friction dominated. With decreasing sediment concentration, vertical particle sorting can result from differential settling, and flows in which this can occur are termed concentrated density flows. The boundary between hyperconcentrated and concentrated density flows is defined by a change in particle behaviour, such that denser or larger grains are no longer fully supported by grain interaction, thus allowing coarse-grain tail (or dense-grain tail) normal grading. The concentration at which this change occurs depends on particle size, sorting, composition and relative density, so that a single threshold concentration cannot be defined. Concentrated density flows may be highly erosive and subsequently deposit complete or incomplete Lowe and Bouma sequences. Conversely, hydroplaning at the base of debris flows, and possibly also in some hyperconcentrated flows, may reduce the fluid drag, thus allowing high flow velocities while preventing large-scale erosion. Flows with concentrations <9% by volume are true turbidity flows (sensuBagnold, 1962), in which fluid turbulence is the main particle-support mechanism. Turbidity flows and concentrated density flows can be subdivided on the basis of flow duration into instantaneous surges, longer duration surge-like flows and quasi-steady currents. Flow duration is shown to control the nature of the resulting deposits. Surge-like turbidity currents tend to produce classical Bouma sequences, whose nature at any one site depends on factors such as flow size, sediment type and proximity to source. In contrast, quasi-steady turbidity currents, generated by hyperpycnal river effluent, can deposit coarsening-up units capped by fining-up units (because of waxing and waning conditions respectively) and may also include thick units of uniform character (resulting from prolonged periods of near-steady conditions). Any flow type may progressively change character along the transport path, with transformation primarily resulting from reductions in sediment concentration through progressive entrainment of surrounding fluid and/or sediment deposition. The rate of fluid entrainment, and consequently flow transformation, is dependent on factors including slope gradient, lateral confinement, bed roughness, flow thickness and water depth. Flows with high and low sediment concentrations may co-exist in one transport event because of downflow transformations, flow stratification or shear layer development of the mixing interface with the overlying water (mixing cloud formation). Deposits of an individual flow event at one site may therefore form from a succession of different flow types, and this introduces considerable complexity into classifying the flow event or component flow types from the deposits.

The physical character of subaqueous sedimentary density flows and their deposits

応用水文 = Applied hydrology

1. Introduction to erosion and dedimentation 2. Physical properties and dimensional analysis 3. Mechanics of sediment-laden flows 4. Particle motion in inviscid fluids 5. Particle motion in Newtonian fluids 6. Turbulent velocity profiles 7. Incipient motion 8. Bedforms 9. Bedload 10. Suspended load 11. Total load 12. Reservoir sedimentation.

Erosion and sedimentation.

FLO‐2D is a two‐dimensional finite difference model that simulates clear‐water flood hazards, mudflows, and debris flows on alluvial fans and urban floodplains. Interactive flood or mudflow routing between channel, street, and floodplain flow is performed using a uniform grid system to describe complex floodplain topography. A quadratic rheological model, developed from field and laboratory mudflow data, enables appropriate simulations of flooding conditions ranging from clear water to hyperconcentrated sediment flows. Computer‐aided design (CAD) graphics of predicted time‐sequenced flood depths automates the delineation of flood hazards. Replication of the 1983 Rudd Creek mudflow in Utah demonstrates the capability of the model.

Two‐Dimensional Water Flood and Mudflow Simulation

A rotational viscometer has been designed for laboratory measurements of the rheological properties of natural mudflow deposits in Colorado. The mudflow matrices comprised of silt and clay particles are sheared under temperature-controlled conditions at volumetric sediment concentrations ranging from 0.10 – 0.45. This study stresses the importance of conducting rheological measurements at low rates of shear because: 1) Those are the conditions found in natural channels; and 2) they avoid the slippage problems observed at large sediment concentrations. At low rates of shear, the Bingham model is fitted to the measured rheograms, and both the viscosity and yield stress increase exponentially with the sediment concentration of the fluid matrix. Both the yield stress and the viscosity increase by three orders of magnitude as the volumetric concentration of sediments in the fluid matrix changes from 10% to 40%. The addition of sand particles does not significantly alter the rheological properties of the matrix unless the volumetric concentration of sands exceeds 0.20.

https://www.engr.colostate.edu/%7Epierre/ce_old/Projects/Paperspdf/O%27Brien-Julien-ASCE88.pdf

Laboratory Analysis of Mudflow Properties

The proliferation of watershed databases in raster Geographic Information System (GIS) format and the availability of radar-estimated rainfall data foster rapid developments in raster-based surface runoff simulations. The two-dimensional physically-based rainfall-runoff model CASC2D simulates spatially-varied surface runoff while fully utilizing raster GIS and radar-rainfall data. The model uses the Green and Ampt infiltration method, and the diffusive wave formulation for overland and channel flow routing enables overbank flow storage and routing. CASC2D offers unique color capabilities to display the spatio-temporal variability of rainfall, cumulative infiltrated depth, and surface water depth as thunderstorms unfold. The model has been calibrated and independently verified to provide accurate simulations of catchment response to moving rainstorms on watersheds with spatially-varied infiltration. The model can accurately simulate surface runoff from flashfloods caused by intense thunderstorms moving across partial areas of a watershed.

Raster‐based hydrologic modeling of spatially‐varied surface runoff

A theoretical investigation of local scour downstream of gradecontrol structures based on twodimensional jet diffusion and particle stability is experimentally verified Turbulent jet diffusion red

/pdf/scour-downstream-of-grade-control-structures-2mx6p6bjyw.pdf

Pierre Y. Julien

Papers

Erosion and sedimentation.

Two‐Dimensional Water Flood and Mudflow Simulation

Laboratory Analysis of Mudflow Properties

Raster‐based hydrologic modeling of spatially‐varied surface runoff

Scour downstream of grade-control structures