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Shields parameter

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Title: Shields parameter  
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Subject: Dimensionless quantity, Deposition (geology), Reynolds number, Atwood number, Magnetic Prandtl number
Collection: Dimensionless Numbers, Fluid Dynamics, Sedimentology
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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. It is given by:

\tau_\ast = \theta = \frac{\tau}{(\rho_s-\rho) g D},

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). ]Application of similarity mechanics and turbulence research on shear flow [Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau (in German) 26. Berlin: Preußische Versuchsanstalt für Wasserbau. 
  • Shields, A. (1936). ]Application of similarity principles and turbulence research to bed-load movement [Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitteilungen der Preußischen Versuchsanstalt für Wasserbau 26. Berlin: Preußische Versuchsanstalt für Wasserbau. 

External links

  • Southard, John. "Chapter 9 – Threshold of movement". Lecture notes – Special topics: An introduction to fluid motions, sediment transport, and current-generated sedimentary structures.  


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