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Application of stochastic models of bed-load transport and dispersion requires a knowledge of the probability distributions of the step lengths and the rest periods of the particles. The probability distributions of the rest periods, the elevation of particle deposition, and the elevation of particle erosion were obtained in a large flume from a continuous record of bed elevation at a fixed point as a continuous function of time. The probability distribution of the step lengths was obtained from a series of instantaneous longitudinal bed profiles and the distribution of the elevation of particle deposition and erosion. Using an existing transport equation, the total sediment transport in the flume was predicted for three flow conditions. The errors in the predicted total sediment transport rates were -3.0%, +3.5%, and +80.1%.

The formation of dunes and antidunes on the erodible bed of an open channel is studied analytically as a problem of stability of the erodible bed. The phase lag existing between the local sediment-transport rate and the local velocity on the bed plays an essential role in the formation of the sand waves. A physical model for the transport of sediment over a wavy bed is presented and a quantitative explanation of this phase lag is developed. The regions of occurrence of dunes of those bed configurations are compared with experimental results previously summarized by Kennedy, the comparison showing a good agreement.

Summary A study aiming to obtain quantitative data on the processes of slope runoff and erosion under arid conditions and relate them to rain and surface properties, was conducted near Elat, in southern Israel. Slope-channel relations, with regard to runoff and sediment transport, were also analysed. Data were obtained by means of three overland flow collectors, two rain recorders and one hydrometric station. The research was conducted over one rain season, during which a single channel flow and five overland flow events occurred. The results lead to the following main conclusions: 1) For a small drainage basin, the threshold values for slopes and channel flow are 3 mm and 5 mm per day, respectively; 2) No clear relation exists between the slope angle and slope runoff and an inverse relation exists between slope angle and slope erosion.

Observations of channel erosion, flow, and sediment transport for the Rio Puerco, in New Mexico, indicate that the characteristics of the channel and of the channel material change rapidly because of deposition and erosion, and that the ephemeral flows carry extremely high concentrations of suspended sediment that influence flow and transport characteristics.

The Einstein bed-load function is used as a basis for developing a procedure for evaluating the capacity of an erodible channel to transport material originating from sources outside the bed and having a size distribution different from that of the bed-material load. The method consists of three elements: (1) Bed-material transport rate and descriptive parameters are computed from the Einstein bed-load function; (2) the moving capacity is computed for each size fraction of the assumed conditions of bed roughness and flow; and (3) for assumed inflow-sediment concentrations and size distributions, the rate of scour or deposition is computed by comparing the inflow rate with the combination of moving capacity and bed-material transport rate. Application of the procedure to the Upper Chenab Canal in West Pakistan illustrates the method of computation and use of the procedure to evaluate the need for sediment control in the design of large alluvial channels.

Review of past studies and investigations, including prototype measurements and hydraulic model tests; reveal some indications of sediment transport and diffusion in the vicinity of the Columbia Estuary and Entrance. These indications reveal a unique pattern of sediment transport and diffusion prevailing in this region. This leads to the conclusion that the estuary is acting as a trap for collection of bottom sediments and that, immediately offshore, the forces of erosion and accretion have established a regime that is also worthy of detailed further study.

The suspension of sediment particles by turbulent eddy diffusion in a nonuniform flow region was studied, using the convective-diffusion equation as a mathematical model. A simplified form of the equation, for which mixing characteristics and flow velocities was assumed uniform, was found to accurately describe the sediment concentration profiles which had been measured in a 24-ft-long flume. Although diffusivities in the nonuniform region tended towards uniformity with downstream distance, the vertical diffusive transport rate was related to depth as a power law function. Measured diffusion coefficients were found to depend on the relative roughness of the mobile bed.

The Truckee River heads in the Sierra Nevada at Lake Tahoe, and terminates in Pyramid Lake. During the 1969 water year, flow about 9 miles upstream from the mouth (974,000 acre-ft) was almost four times the long-term average, due mainly to heavy winter rains and spring snowmelt. A short period of low-altitude rainfall produced the highest concentrations of suspended sediment, whereas a much longer subsequent period of snowmelt yielded a much greater total quantity of material. The upper 90 percent of the basin yielded about 260 acre-feet (630,000 tons) of sediment at the Nixon gage, whereas an estimated 2,800 acre-feet (6.8 million tons) was contributed by erosion of about 200 acres of river bank below the gage. Solute content at the gage ranged from 80 to 450 mg/l, dominated by calcium, sodium, and bicarbonate, plus silica in the most dilute snowmelt and chloride in the most concentrated low flows. Solute load totaled about 130,000 tons, of which the principal constituents in Pyramid Lake-sodium plus equivalent bicarbonate and chloride-amounted to almost 40,000 tons. The total solute load during a year of average flow may be 45,000-55,000 tons, including 18,000-22,000 tons of principal lake constituents.

A detailed echo-sounding survey of Tremadoc Bay, northern Wales, shows sand waves occurring in the southeastern corner of the Bay. These are markedly asymmetrical and indicate mass water and sediment movement through a localised “deep” at the landward end of Sarn Badrig, a shoal extending some 10.5 miles southwestwards into Cardigan Bay. It is suggested that the Sarn forms an effective barrier to water movement over the greater part of its length, causing water to “pond up” in the eastern part of Tremadoc Bay under the influence of westerly winds. This water escapes southwards through the inshore channel and in doing so may actively erode the sea floor.

Channels constructed in coarse alluvial material tend to develop an armor coat at the bed's surface protecting the material beneath the top layer from further erosion. A method is outlined which permit the prediction of the eroded material. Based on these results, it is possible to make an estimate on the minimum amount of material to be eroded prior to development of a stable condition resulting from amoring. An attempt is made to determine those condition which result in a finally stable bed. This leads to a design criterion for stable channels constructed in coarse nonuniform alluvial material. This design criterion integrates the stabilizing influence of all grain sizes present in a self-stabilized armor coat and permits operating the channel at a preset factor of safety.

In this thesis first a general derivation is given of the 'macro'-equations of mass- and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture. In particular, attention is paid to a) the attenuation of viscous-momentum transfer from the boundary to the interior of a granular bed subject to a surface flow, b) the drag and lift forces exerted by a turbulent shear flow on particles of the bed surface, and, c) the balance of forces acting on a bed load under uniform-flow conditions. It is shown that filter flow driven by shearing along the boundary of a granular sediment bed exerts a drag force on a layer of only two or three particle diameters within the bed. A drag force on the bulk mass of sediment is only exerted by a pore-pressure gradient. Stability conditions are formulated for a loose granular bed subject to erosive flow, at SHIELDS' grain-movement condition and dUring bed-load transport. 'Macro'-stresses acting along 'wavy' surfaces parallel to the bed are defined for that purpose, and an attenuation factor is introduced for the transmission of turbulent fluid shear from the surface towards the interior of the bed. It is shown that SHIELDS' dimensionless expression for the critical bed shear stress at the threshold of continuous sediment motion, 1/Phi , must reach a constant value for low-shear Reynolds' numbers (Re* < O. 5), as long as there is no cohesion between the particles. It is concluded that the bed load, consisting of particles rolling and saltating over the bed, must reduce the maximum turbulent fluid shear at the bed surface, at sufficiently high bed shear stress, to the critical threshold drag that would lead to the initiation of non-ceasing scour.

In this thesis first a general derivation is given of the 'macro'-equations of mass- and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture. In particular, attention is paid to a) the attenuation of viscous-momentum transfer from the boundary to the interior of a granular bed subject to a surface flow, b) the drag and lift forces exerted by a turbulent shear flow on particles of the bed surface, and, c) the balance of forces acting on a bed load under uniform-flow conditions. It is shown that filter flow driven by shearing along the boundary of a granular sediment bed exerts a drag force on a layer of only two or three particle diameters within the bed. A drag force on the bulk mass of sediment is only exerted by a pore-pressure gradient. Stability conditions are formulated for a loose granular bed subject to erosive flow, at SHIELDS' grain-movement condition and dUring bed-load transport. 'Macro'-stresses acting along 'wavy' surfaces parallel to the bed are defined for that purpose, and an attenuation factor is introduced for the transmission of turbulent fluid shear from the surface towards the interior of the bed. It is shown that SHIELDS' dimensionless expression for the critical bed shear stress at the threshold of continuous sediment motion, 1/Phi , must reach a constant value for low-shear Reynolds' numbers (Re* < O. 5), as long as there is no cohesion between the particles. It is concluded that the bed load, consisting of particles rolling and saltating over the bed, must reduce the maximum turbulent fluid shear at the bed surface, at sufficiently high bed shear stress, to the critical threshold drag that would lead to the initiation of non-ceasing scour.

The planimetric shape of Wreck Bay has been studied by fitting various segments of the bay to theoretical logarithmic spiral curves, and by using the characteristics of incident swell to estimate longshore sediment transport along the beach. We have found that the cliff base in the northwest half of the bay closely follows log-spiral curvature, whereas the southeast half reflects only poor correspondence. This situation is due largely to distortion of the incident swell by two islands in the bay, Florencia Is., and Seal Rock. Quasi-permanent cliff sections supporting large trees occur on the landward side of the theoretical log-spiral curves, and those sections exposing unconsolidated glaciofluvial outwash are generally seaward of the curves. Present day erosion, due mainly to wind action on the exposed parts of the cliff, indicates that gradual mutation of the planimetric shape, particularly for the southeast half of the bay, is tending towards an improved fit. Longshore current distribution along the beach accounts for the direction of spit-bar growth at the mouth of Lost Shoe Creek, and also for the presence of Sand Point in the middle of the bay. It has been found useful when comparing the goodness of fit of beaches of different lengths to introduce a normalized root mean squared error. Furthermore, it has been shown that if a headland remains part of a receding spiral beach, then the spiral center must gradually migrate away from the headland as erosion proceeds.

Problems in which Bureau of Reclamation has experienced need for more research; transport and deposition in channels; unmeasured or bedload; channel stability; deposition behind structures; channel degradation.

The mean particle size of sediment carried on the bed of the Columbia River increases downstream. The Snake River and other upstream tributaries contribute mostly fine sediment carried in suspension. Many downstream tributaries produce coarser sediment, which is carried largely in the bedload. Bedload is appreciable only in the lower portions of the river, and is a small percentage of the suspended load Large migrating sand waves form the top surface of the bed. The distribution of sediment on some of the reservoir floors changes throughout the year. Sediment deposited during low discharges may be scoured from the reservoirs during periods of high discharge and transported downstream through the dams. The amount of sediment transported by the Columbia River system during a single flood may exceed that which is transported during an entire "average" year. The mineral and chemical composition of Columbia River sediment obtained from reservoir floors suggests that the sediment particles have undergone relatively little chemical weathering. Chemically unstable mineral grains and lithic fragments abound. Quartz and elements considered relatively immobile during chemical weathering show no obvious enrichment in the sediment. The ratio of quartz to all "unstable" constituents (feldspars, mafic minerals, and lithic fragments) decreases downstream, whether the latter are taken individually or as a group. Columbia River sediment is apparently derived from two principal sources: the upstream sediment from surficial deposits is derived ultimately from metamorphic, plutonic, and sedimentary rocks; and downstream sediment is derived largely from the erosion of andesitic volcanic rocks and sediments. The upstream sediment is fine grained and is transported by the Columbia in suspension. The volcanic sediment is coarser and generally forms the bedload. It is likely that these two sediment types remain more or less physically separated during transport and deposition.

The Chehalis River drains an area of about 2,100 square miles in southwestern Washington of which 1,813 square miles is in the study area. The average annual suspended-sediment discharge from the area during the study period (water years 1962-65) was about 540,000 tons; annual loads ranged from 270,000 to 690,000 tons. About 74 percent of the suspended-sediment discharge was derived from the Satsop and Wynoochee River drainage basins which together cover about 450 square miles. Only about 24 percent was carried by the Chehalis River past Porter above which the drainage area is 1,294 square miles. Estimated average annual suspended-sediment yield from tributary basins ranged from 20 to 1,500 tons per square mile. Variability in sediment yield throughout the Chehalis River basin is attributed both to areal differences in the quantity and intensity of runoff during storm periods and to the variable quantities and characteristics of the sediment available for transport. These factors, in turn, are controlled by geologic and climatic factors and by land-use practices. Most sediment transported in the basin originates from channel erosion which occurs mostly during storm runoff. During the study period, 90 percent of the suspended-sediment discharge occurred only 5-10 percent of the time at headwater sampling sites and 15-20 percent of the time at the lower main-stem stations. Observed sediment concentrations ranged from less than 1 milligram per liter to 1,220 milligrams per liter, and greatest concentrations were associated with tributary basins of highest yield.

EROSION and transportation of sediment by organic agents is a well-known phenomenon, and sediment transport is known to occur over large areas in many parts of the world1. However, the best-known examples of organic transportation are confined almost exclusively to coarse-grained sediments. We know of no well-substantiated examples of transport of sediment finer than coarse sand over distances greater than a few centimetres.

When a grain of sand is delivered to the sea by erosion it begins a journey being transported along beaches or bars, or offshore by waves and currents. The history of this journey can be extremely complex for the grain might spend a few seconds in one place and many years trapped in another before being released again for travel. It is therefore important at the outset to place some limitations upon our study. Firstly, our time scale is limited to the past seventy years, the time over which data were gathered. Secondly, the geographical position is limited to a strip of the east coast of Cape Cod 29,400 yards in length (Figure 1), extending seaward to where water depth is about forty feet. After a grain of sediment leaves this area we are no longer concerned with it. We define residence time as the average number of years a grain of eroded sediment is likely to spend in this prescribed area before it is transported elsewhere. We will further try to show that sediment takes a preferred path, some of it moving along the beach and some along the bars. It makes no difference to us if specific environments share grains; that is to say, some material will be on the beach one day and on the bar the next. In the end those grains which tend to be more stable in the beach environment will spend more time there and will travel with a characteristic velocity which is different from the velocity of those grains which are in hydrodynamic equilibrium on bars. The method used to compute residence time involves volume stability. We measured the volume of the beaches and bars in the definition area and assumed that these volumes have not changed within the time limits of our study. We also measured the yearly addition of sediment to the area. In-as-much as there is neither gain nor loss of the average volume of sand -built features, i.e., the beaches and bars, sand must be moving out of the study area at the same rate it is being introduced. Therefore, the residence time in years is the average volume of a beach or bar divided by the yearly volume of sediment added by erosion to the beach or bar.

Barrier islands migrate along some coastal areas in the direction of dominant sediment transport. At the forward end of the island deposition occurs on the margin of the channel where the environment strongly influences the characteristics of barrier-island deposits. The depth of the channel, for example, exceeds two-to-three times that of other environments associated with barrier deposits. Moving along the coast, the channel erodes and reworks the deposits of other environments. The reworked area extends landward and seaward of the inlet and is several miles wide. The depth of reworking and the subsequent deposition preclude further modification by other agencies of the barrier-island environment. The erosion that accompanies transgression and regression may remove the upper level of barrier deposits, leaving modified channel sediments for interpretation and identification. Sedimentary modifications produced by island migration include textural changes, gross shape of the deposit, and steepening and reorientation of stratification. Recognition of the reorientation of stratification is particularly important in paleocurrent analysis. Modified channel sediments inter-finger seaward with shallow neritic deposits and landward with lagoonal salt-marsh sediments. Although the duration of the Holocene high stand of the sea was too short to permit major migration-modification of Holocene islands, there was probably enough time for the extensive reworking of many ancient deposits. Studies on channel sediments and on the extent of island migration can provide information on the environment during the deposition of coastal sediments.