Shields parameter

The Shields parameter, also called the shields criterion or shields number, is a nondimensional number used to calculate the initiation of motion of sediment in flowing water. It is a nondimensionalization of a shear stress, and is typically denoted $\tau *$ or $\theta$. It is given by:

$\tau *=\theta ={\frac {\tau }{(\rho _{s}-\rho )gD}}$

where

$\tau$ is a dimensional shear stress

$\rho _{s}$ is the density of the sediment

$\rho$ is the density of water

$g$ is acceleration due to gravity

$D$ is mean particle diameter of the sediment

Physical meaning:

By multiplying the top and bottom of the Shields parameter by d^2, you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle. The effect of the density ratio ρs/ρ is still unclear, but is known not to be large, and anyway most sediment problems involve quartz-density sediment in water.

References

Cao, Zhixian; Pender, Gareth; Meng, Jian (2006). "Explicit Formulation of the Shields Diagram for Incipient Motion of Sediment". Journal of Hydraulic Engineering. 132: 1097. doi:10.1061/(ASCE)0733-9429(2006)132:10(1097).

http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-special-topics-an-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/lecture-notes/ch9.pdf