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 a fluid flow. It is a nondimensionalization of a shear stress, and is typically denoted $\tau _{\ast }$ or $\theta$. This parameter has been developed by Albert F. Shields, and is called later Shields parameter. The Shields parameter is the main parameter of the Shields formula. It is given by:

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

where:

• $\tau$ is a dimensional shear stress;
• $\rho _{s}$ is the density of the sediment;
• $\rho$ is the density of the fluid;
• $g$ is acceleration due to gravity;
• $D$ is a characteristic particle diameter of the sediment.

Physical meaning

By multiplying the top and bottom of the Shields parameter by D², you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.

References

• Shields, A.. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung [Application of similarity mechanics and turbulence research on shear flow] (PDF). Mitteilungen der Preußischen Versuchsanstalt für Wasserbau (in German). Vol. 26. Berlin: Preußische Versuchsanstalt für Wasserbau. Archived from the original on 2011-07-18.
• Shields, A. (1936). "Application of similarity principles and turbulence research to bed-load movement (translated version)". Caltech Library. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau. 26. Berlin: Preußische Versuchsanstalt für Wasserbau.

External links

• Southard, John. "Chapter 9 – Threshold of movement" (PDF). Lecture notes – Special topics: An introduction to fluid motions, sediment transport, and current-generated sedimentary structures. MIT Open Courseware. Archived from the original (PDF) on 2011-06-29. Retrieved 2011-01-31.