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 form of non-dimensionalization of a shear stress, and is typically denoted ${\displaystyle \psi }$ or ${\displaystyle \theta }$. 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. The Shields parameter is given by:

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

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.

The critical shear stress and also the critical Shields number (${\displaystyle \tau _{\ast }}$ and ${\displaystyle \theta _{\ast }}$) describe the conditions when the sediment starts moving. Note that the shear stress is a property of the current, while the critical shear stress is a property of the sediment.

By multiplying the top and bottom of the Shields parameter by ${\displaystyle D^{2}}$, you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.

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

• 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.
• Schiereck, Gerrit Jan (2012). "ch2 and 3". Introduction to bed, bank and shoreline protection. Delft, Netherlands: Delft Academic Press. ISBN 978-90-6562-306-5. Retrieved 2024-08-25.

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