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A Phenomenological Study of Sediment Transport in Shallow Overland Flow

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A Phenomenological Study of Sediment Transport in Shallow Overland Flow A PHENOMENOLOGICAL STUDY OF SEDIMENT TRANSPORT IN SHALLOW OVERLAND FLOW M. J. M. Römkens, S. M. Rao, S. N. Prasad ABSTRACT. Soil erosion is a highly complicated phenomenon consisting of many component processes. On upland areas, these processes are usually thought of as detachment and transport of soil particles by rainfall and surface flow. One of the most difficult processes to quantify is sediment transport. This process depends on a host of factors including sediment type, size, size distribution, and concentrations on one hand and the flow regime relative to rates and velocities on the oth- er hand. The effect of all of these factors is influenced by soil surface cover and surface roughness conditions. The Na- tional Sedimentation Laboratory has in recent years conducted a series of basic laboratory studies to better understand sediment movement in shallow overland flow. These experiments involved super-critical flow regimes in a 7 m long and 10 cm wide channel in which sand-size material was seeded at the upstream end at controlled rates in a super-critical flow regime with Froude numbers >1. Particle sizes were coarse sand (1000 to 1400 μm), medium sand (600 to 850 μm), and spherical glass beads (600 to 1000 μm). Measurements included particle velocity and particle concentrations using pho- tonic probes. Three modes of transport were noted: a saltation mode at low concentrations, sediment waves in which sed- iment moved in regularly spaced waves, and a meander mode. The latter two modes were attributed to particle interac- tions. The transported sediment was continuously collected at the downstream end by a rotating sampler. A curvilinear increase in transport rate was noted with an increase in seeding rate until a critical saltation limit was reached, after which a decrease in sediment movement occurred with the formation of organized sediment structures. The small struc- tures were waves with spacings of the order of magnitude of tens of particle diameter, while the larger-scale meander had wavelengths of hundreds of particle diameters. The measured pseudo-equilibrium transport rates were smallest in the me- ander mode, followed by the wave mode. A relationship was obtained that described the transition from the saltation mode to the wave mode in terms of a critical solid concentration. Keywords. Bed load transport, Saltation, Sediment movement, Sediment particle interactions, Shallow overland flow, Soil erosion. ediment movement was studied in the past for both Sekine and Kikawa (1992) and Niño et al. (1994) studied subcritical and supercritical flows (Froude number stochastic methods describing grain collisions with the >1). Among those, subcritical flows usually con- streambed. Francis (1973) studied saltation of solitary S cerned channel flows. Shallow overland flow is grains to estimate the particle velocity and its dependence commonly identified with supercritical conditions where on other parameters such as terminal velocity and the the roll waves on the free surface influence the movement transport stage, defined as the ratio of the shear velocity to of grains on the channel bed. Saltation has long been terminal velocity. He indicated that the presence of adjacent known as a sequence of ejection and downward trajectory grains could change the resistance with travel at slower motions of individual sediment particles under the influ- speeds. Bagnold (1966) and Francis (1973) found that the ence of gravity and the interstitial fluid motion (Bagnold, saltation trajectories were unaltered by turbulence over a 1966; Francis, 1973; Abbott and Francis, 1977). Many re- rough bed, although a slight modification of the saltation searchers have adopted experimental, analytical, and nu- trajectory from a parabolic to wave profile was observed. merical methods to describe the saltation mechanism. Abbott and Francis (1977) studied incipient saltation, the mechanism of impact collisions with the bed surface, and flow depth and determined the trajectory dimensions. More recently, Ancey et al. (2002) found that the ratio of shear Submitted for review in February 2012 as manuscript number SW 9661; approved for publication by the Soil & Water Division of stress to particle weight above 0.03 makes particles in the ASABE in September 2012. Presented at the 2011 Symposium on Erosion size range from 3 to 6 mm saltate on a rough, fixed bed and Landscape Evolution (ISELE) as Paper No. 11045. made up of similar particle sizes. The USDA is an equal opportunity provider and employer. The authors are Mathias J. M. Römkens, ASABE Member, Labora- The initial rotational mode of moving particles on a bed tory Director, USDA-ARS National Sedimentation Laboratory, Oxford, is known as rolling. For small particles (Reynolds number Mississippi; S. Madhusudana Rao, Research Assistant Professor, and <10), the solitary grain motion experiments of Charru et al. Shyam N. Prasad, Research Professor (retired), Department of Civil En- (2007) showed that at high fluid shears particles travel fast- gineering, University of Mississippi, Oxford, Mississippi. Corresponding author: Mathias J. M. Römkens, USDA-ARS National Sedimentation er over smooth beds than rough beds. Ramesh et al. (2011) Laboratory, P.O. Box 1157, Oxford, MS 38655; phone: 662-232-2940; e- studied solitary grain movement on a rough bed using high- mail: [email protected]. Transactions of the ASABE Vol. 56(2): 515-522 2013 American Society of Agricultural and Biological Engineers ISSN 2151-0032 515 speed imaging techniques. They found that larger particles Briefly, shallow overland flow was simulated in the laborato- travel faster in the initial mode of motion due to rolling, ry on a 7 m long × 10 cm wide aluminum channel. The whereas lighter particles with lower densities travel faster channel had two optical probes inline with the flow that rec- in the saltation mode. Based on numerical computations of orded electronic signals as particles passed through the field the equations of motion of saltating particles, van Rijn of vision. The photonic probes enabled particle or solid con- (1984) proposed semi-empirical expressions to estimate the centrations and velocity measurements. Digital photographs saltation height, saltation length, particle velocity, and the complemented the grain flux data obtained with the optical bed load concentration. probes. The channel was slightly inclined at <1°. Water flow Parameters that have not been adequately discussed in was regulated by rotameters that were installed in the water the aforementioned studies concern particle fluxes and the line at the upstream end of the channel. Saltation measure- particle interaction effect on sediment movement. Francis ments were made with three particle sizes: coarse sand (ds -3 (1973), Abbott and Francis (1977), Ancey et al. (2002), and range = 1000 to 1400 μm; ρs = 2,516 kg m ), medium sand -3 Ramesh et al. (2011) designed and developed sediment (ds range = 600 to 850 μm; ρs = 2,667 kg m ), and spherical transport by seeding solitary grains into a stream. Niño et -3 glass beads (ds range = 600 to 1000 μm; ρs = 2,219 kg m ). al. (1994) and Lee and Hsu (1994) conducted experiments The particle sizes were chosen as representative sizes of soil with many grains added to the flow. There is no particle in- material in runoff from agricultural land. These sizes were teraction in solitary grain flow experiments, although colli- also larger than the thickness of the boundary layer, thus re- sions with the boundary are present. As the seeding rate in- ducing the complexity of the analysis. The grain sizes were creases, particles interact, the grain velocity and transport seeded into the channel stream by means of a vibrating feed- mode may change, and transport is affected. Papanicolaou er and hopper arrangement near the upstream end. The fre- et al. (2003) observed clusters of various geometrical con- quency and amplitude controllers of the feeder and hopper figurations depending on the availability of sediment on the allowed any desired grain addition rate. A rotating sampler stream bed. Suryadevara et al. (2004) and Prasad et al. (Rao et al., 2007) at the downstream end enabled us to record (2009) seeded grains of different sizes at increasing rates in the transport rates of the stream bed. constant flow regimes and observed changes in the sedi- Our saltating experiments were conducted mostly for two ment transport mode depending on the sediment concentra- volumetric water flow rates of 15.7 and 21.6 L min-1. These tion. Their findings indicated different modes of transport flow rates correspond to Froude numbers (Frl = U/√gH) of at different grain or solid concentrations consisting of salta- 1.45 and 1.92, respectively. The Reynolds numbers for these tion, sediment waves, and meanders. The experimental two flows were 2291 and 3102, respectively. The solid con- findings were obtained with grain sizes larger than the centration (αs) is the non-dimensional representation of the thickness of the boundary layer. Their study was also com- areal coverage of grains from the field of vision in the chan- plemented with analytical considerations based on a two- nel stream and ranged between 0 and 1. The lower and upper layer flow model, consisting of a sediment zone in which bounds of the calibration referred to the grain-water mixture the conservation of mass and momentum equations were for no particles and for close packing, respectively. The grain used and a sediment free zone in which the St. Venant velocity was estimated from the cross-correlations of the equations were used. In this article, we focus on the transi- twin probe signals. The sampling periods for concentration tion from the saltation phase to the sediment wave phase, and velocity signals were 60 s and 500 ms, respectively. Sol- which is the critical point at which the maximum transport id concentration data were complemented with digital photo- capacity is reached for the conditions of this flow regime graphic information.
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