Analysis of bedload transport in laminar flows

Nian-Sheng Cheng
School of Civil and Environmental Engineering, Nanyang Technological
University, Nanyang Avenue, Singapore 639798,

        Bedload transport generally depends on the bed shear stress and 
Reynolds number. However, knowledge of the Reynolds number effect on the 
transport rate is relatively limited because many sediment transport problems 
are often studied only for the condition of turbulent flows. As an extreme 
case to reflect the viscous effect on sediment transport, sediment transport 
in laminar flows is considered in this paper. A stochastic approach is 
adopted to explore how the transport rate can be associated with 
characteristics of laminar flows. First, the probability of erosion in 
the absence of turbulence is assumed to depend only on the randomness of bed 
particles. The probability is then applied to formulate the sediment 
transport rate, of which the derivation is made largely based on the 
Einstein's bedload theory. The theoretical result indicates that the 
dimensionless transport rate for laminar flows is dependent on the 
dimensionless shear stress and dimensionless particle diameter or the 
shear Reynolds number. Comparisons are finally made between the derived 
formula and an empirical correlation available in the literature.