# 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.