Critical Shields Number Research Articles

Experimental Study on Bed Load Transport of Shell fragment-Mixed Sand under Waves

Beneficial use of shell for constitutive materials of beach is proposed instead of its disposal. Since the shape of shell fragment is oblate, the knowledge on littoral drift of sand with spherical shape could not be applied directly for understanding of its behavior under waves. In this study, critical shields number and fall velocity of shell fragment are evaluated changing oblate shapes of the fragments, and the characteristics of bed load transport of shell and shell-mixed sand beds are examined by a movable-bed experiment. From the experiments, the effects of oblateness on the increase of resistance to wave and current are elucidated. It is found that the interaction of sand and shell on their movements has an effect on the bed - load rate changing the height of sand ripples.

Three‐dimensional CFD modeling of morphological bed changes in the Danube River

The bed changes in a section of the river Danube were computed using a 3‐D computational fluid dynamics model. A time series of discharges during the flood in 2002 was used. The results compared reasonably well with regular bed level surveys before and after the flood. The Danube River section was 6 km long and located between Vienna and the Austrian‐Slovakian border. The fully three‐dimensional numerical model solved the Navier‐Stokes equations using the k‐epsilon turbulence closure. Nonuniform sediment transport was computed using the formulas of Wu et al. (2000b), considering hiding‐exposure algorithms. Both bed deformation and sorting processes were calculated. A number of parameter sensitivity tests were carried out on roughness values, parameters in the sediment transport capacity formula, parameters in the hiding‐exposure formulas, critical Shields number, and variations in the formulas for the effect of a sloping bed. Additionally, the sediment inflow to the section was varied together with investigations of physical parameters such as vegetation and groyne structures. The results were most sensitive to the Shields number for critical movement of the sediments. An error analysis was performed to give a quantitative assessment of the parameter sensitivity tests.

Variation of the critical Shields number with slope

Variation of the critical Shields number with slope

Physical basis for quasi‐universal relations describing bankfull hydraulic geometry of single‐thread gravel bed rivers

We examine relations for hydraulic geometry of alluvial, single‐thread gravel bed rivers with definable bankfull geometries. Four baseline data sets determine relations for bankfull geometry, i.e., bankfull depth, bankfull width, and down‐channel slope as functions of bankfull discharge and bed surface median sediment size. These relations show a considerable degree of universality. This universality applies not only within the four sets used to determine the forms but also to three independent data sets as well. We study the physical basis for this universality in terms of four relations, the coefficients and exponents of which can be back calculated from the data: (1) a Manning‐Strickler‐type relation for channel resistance, (2) a channel‐forming relation expressed in terms of the ratio of bankfull Shields number to critical Shields number, (3) a relation for critical Shields number as a function of dimensionless discharge, and (4) a “gravel yield” relation specifying the (estimated) gravel transport rate at bankfull flow as a function of bankfull discharge and gravel size. We use these underlying relations to explore why the dimensionless bankfull relations are only quasi‐universal and to quantify the degree to which deviation from universality can be expected. The analysis presented here represents an alternative to extremal formulations to predict hydraulic geometry.

Determination of the critical Shields number for particle erosion in laminar flow

We present reproducible experimental measurements for the onset of grain motion in laminar flow and find a constant critical Shields number for particle erosion, i.e., θc=0.12±0.03, over a large range of small particle Reynolds number: 1.5×10−5⩽Rep⩽0.76. Comparison with previous studies found in the literature is provided.

A field experiment on streambed stabilization by gravel structures

We report an experiment to study particle restraint imposed by bed surface aggregate structures in a small headwater stream. Extant structures (clusters, stone lines, and partial stone cells) were manually destroyed in one reach of the channel (treated reach) whilst leaving them intact in an adjacent reach (reference reach), establishing two reaches of similar sediment texture and gradient that differed primarily in degree of structure development. After the first flood, the sediment yield from the treated reach was 32% greater than from the reference reach. For material > D 84, the treated reach yielded 24× that from the reference reach. The critical Shields number was reduced by more than 18% in the treated reach to the value generally accepted for loose, heterogeneous sediment. The effect of structural development on particle mobility was subsequently studied in the treated reach over the course of three flow events that did not significantly exceed the Shields threshold, so that bed material transport remained low. After these events, mobility of the larger clasts was substantially reduced, permitting the inference that particle restraint in the treated reach approached that of the reference reach. This corresponds with direct evidence of structure development in the treated reach as indicated by the movement and emplacement of marked grains. A major flood, however, caused a reversion toward unstructured conditions in the treated reach, indicating that structures had not developed the resilience exhibited in the reference reach.

Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow

The transport inception of immersed grains is studied experimentally with laminar flow conditions in a Hele-Shaw cell when varying the tilt angle of the cell and the water flow rate. Varying these two parameters, grains are either motionless, rolling on the bed surface, or avalanching downwards. This paper focuses on the determination of the onset for grain motion either by erosion or by avalanche. For a horizontal interface, onset for erosion corresponds to a constant critical Shields number θc=0.14 at small particle Reynolds number (Red<1) but decreases as Red−1 at larger particle Reynolds number (Red>1). For tilted bed, the onset of erosion increases when the flow is opposed to gravity. Both results are compared to a standard model based on a balance of the forces acting on a single grain lying on a tilted plane. When tilt angles are large, avalanches occur. The maximum angle of stability is modified by the flow and increases slightly when the flow acts against gravity. This behavior is compared to a continuous model where a few layers of grains are about to slide.

Threshold relations for the transport of sediment by overland flow on desert hillslopes

AbstractAlthough the Shields relation was developed for rivers, it has been applied to sediment transport by overland flow. According to the Shields relation, where the critical boundary Reynolds number Re*c exceeds 40, the critical Shields number F*c is independent of both Re*c and the ratio of the critical flow depth to particle diameter dc/D. Analyses of data collected from runoff plots in southern Arizona reveal that F*c is positively correlated with both Re*c and dc/D. Thus the Shields relation does not apply to overland flow on debris‐covered desert hillslopes.Multiple regression analysis is employed to develop alternative threshold relations in which critical boundary shear stress τc is related to D and dc/D (R2 = 0.782) and to D and Sc (critical gradient) (R2 = 0.625). The computed R2 values derive in large part from the spurious correlations of dc/D and Sc with τc. Nevertheless, the relations may be utilized to predict τc. In this regard, the latter relation is likely to prove more useful than the former because Sc is generally known, whereas dc is not.An investigation of the functional relation between τc and D reveals that τc varies approximately with D2 for overland flow on the desert hillslopes under study, whereas the Shields relation predicts a linear relation (i.e. a D exponent of 1). This result is consistent with Cheng's data which show that F*c varies with (dc/D)−1 where 0.4 < dc/D < 2 and may be explained in terms of increased energy dissipation both in separation zones downslope of particles and in distortion of the water surface as dc/D decreases. Consequently, larger values of τc, and hence F*c, are required to initiate the transport of particles of a given size D as dc decreases.

Prediction of average mixing depth of sediment in the surf zone

A predictive model for the average depth of mixing of sediment in the surf zone is formulated on the basis of the wave-induced shear stress on the bottom. The model is calibrated using field data obtained through tracer experiments performed on Pacific beaches of Japan. The result gives Z ̄ D = 81.4 (Ψ b − Ψ c ) , where Z ̄ is the average depth of sediment mixing in the surf zone, D is the grain size of the sediment, Ψ b is the Shields parameter at the wave breaking point, and Ψ c is the critical Shields number for oscillatory flow. The predicted mixing depth is found to increase in an approximately linear fashion with the breaking wave height for significant breaking wave heights up to about 1.5 m. For greater breaking wave heights, the rate of increase in the mixing depth decreases with increasing wave height. The mixing depth is also a strong function of the wave period in the larger wave height region. Finally, the predicted mixing depth is found to be a weakly increasing function of the sediment grain size.