An examination of dimensionless variables in sediment threshold studies

Shields dimensionless stress and particle Reynolds number have been used since their introduction into sediment threshold studies. They do not separate forcing and resisting quantities so that both shear velocity and particle grain size occur in each. This study considers two different combinations of those traditional parameters to give two dimensionless variables, a dimensionless grain size independent of flow, and a dimensionless shear stress independent of the size. Considering observed data from various sources, the scatter around the new dimensionless threshold curve was found to be less than around the traditional Shields form. Simple explicit rational approximations were obtained between the new dimensionless stress and dimensionless grain size. They describe experimental results better than arbitrary formulae for the traditional Shields parameter. That, with the separation of flow and resistance, makes the solution of practical problems simpler.