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 [math]\displaystyle{ \tau_\ast }[/math] or [math]\displaystyle{ \theta }[/math]. 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:

[math]\displaystyle{ \tau_\ast = \theta = \frac{\tau}{(\rho_s-\rho) g D}, }[/math]

where:

• [math]\displaystyle{ \tau }[/math] is a dimensional shear stress;
• [math]\displaystyle{ \rho_s }[/math] is the density of the sediment;
• [math]\displaystyle{ \rho }[/math] is the density of the fluid;
• [math]\displaystyle{ g }[/math] is acceleration due to gravity;
• [math]\displaystyle{ D }[/math] 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) (in de). Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau. 26. Berlin: Preußische Versuchsanstalt für Wasserbau. http://resolver.tudelft.nl/uuid:61a19716-a994-4942-9906-f680eb9952d6. 
• Shields, A. (1936). "Application of similarity principles and turbulence research to bed-load movement (translated version)" (in en). Caltech Library. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau (Berlin: Preußische Versuchsanstalt für Wasserbau) 26. http://resolver.tudelft.nl/uuid:a66ea380-ffa3-449b-b59f-38a35b2c6658. 

External links

• Southard, John. "Chapter 9 – Threshold of movement". MIT Open Courseware. 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.