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 ${\displaystyle \theta }$. 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:

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

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.