The Rouse number (P or Z) is a non-dimensional number in fluid dynamics which is used to define a concentration profile of suspended sediment and which also determines how sediment will be transported in a flowing fluid.
and the upwards velocity on the grain as a product of the von Kármán constant
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.