The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment

Sediment

Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....

 in a fluid flow. It is a nondimensionalization of a shear stress

Shear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

, and is typically denoted or . It is given by:


where:

	is a dimensional shear stress;
	is the density of the sediment;
	is the density of the fluid;
	is acceleration due to gravity;
	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.