Entrainment Probabilities of Mixed-Size Sediment Incorporating Near-Bed Coherent Flow Structures

Abstract

In this work we incorporate the effect of near-bed coherent flow structures into the entrainment of randomly configured mixed-size sediments. The fourth-order Gram–Charlier type probability density function (GC pdf) of near-bed streamwise velocity is employed to account for the higher-order correlations associated with turbulent bursting. A compilation of the published data over a wide range of bed roughness is used to analyze the near-bed coherent flow structures, including the second-, third-, and fourth-order moments of velocity fluctuation (i.e., turbulence intensity, skewness, and flatness factors) required in the fourth-order GC pdf. An important result of this study is a set of quantitative relations used to predict these higher-order moments as a function of the roughness Reynolds number. The random grain protrusion is parameterized with the exposure and friction heights, and an existing probabilistic approach is used to correct the hiding effect of mixed-size sediment. The above factors are all incorporated into the formulation of entrainment (rolling and lifting) probabilities. As compared to the previous normal and lognormal models, the present results demonstrate significantly improved agreement with the observed data for the unisize and mixed-size sediments under partial- and full-transport conditions. The results also reveal that the third-order GC pdf can be used to approximate the fourth-order one for the fully rough beds, however, for smooth beds the fourth-order GC pdf should be used to adequately incorporate the effects of higher-order correlations. This paper offers some new insights into the processes of sediment entrainment.