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 ${\displaystyle \tau _{\ast }}$ or ${\displaystyle \theta }$. It is given by:

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

where:

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