Rouse number explained

w _{s} and the upwards velocity on the grain as a product of the von Kármán constant \kappa and the shear velocity u _{*} .P = (w _{s})/(\kappa u _{*})

Occasionally the factor β is included before the von Kármán constant in the equation, which is a constant which correlates eddy viscosity to eddy diffusivity. This is generally taken to be equal to 1, and therefore is ignored in actual calculation. However, it should not be ignored when considering the full equation.

P = (\beta w _{s})/(\kappa u _{*})

It is named after the American fluid dynamicist Hunter Rouse. It is a characteristic scale parameter in the Rouse Profile of suspended sediment concentration with depth in a flowing fluid. The concentration of suspended sediment with depth goes as the power of the negative Rouse number. It also is used to determine how the particles will move in the fluid. The required Rouse numbers for transport as bed load, suspended load, and wash load, are given below.

Mode of Transport	Rouse Number
Bed load	>2.5
Suspended load 50% Suspended	>1.2, <2.5
Suspended load 100% Suspended	>0.8, <1.2
Wash load	<0.8

See also

• Sediment transport
• Sediment
• Dimensionless quantity

References

• Whipple, K. X (2004), 12.163 Course Notes, MIT Open Courseware. https://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-163-surface-processes-and-landscape-evolution-fall-2004/lecture-notes/4_sediment_transport_edited.pdf