Dimensionless argument: a narrow grain size range near 2 mm plays a special role in river sediment transport and morphodynamics

Abstract. The grain size 2 mm is the conventional border between sand and gravel. This size is used extensively, and generally without much physical justification, to discriminate between such features as sedimentary deposit type (clast-supported versus matrix-supported), river type (gravel-bed versus sand-bed) and sediment transport relation (gravel versus sand). Here we inquire as to whether this 2 mm boundary is simply a social construct upon which the research community has decided to agree via repetition, convergence and rearticulation, or whether there is some underlying physics. We use dimensionless arguments to show the following for typical conditions on Earth, i.e., natural clasts (e.g. granitic or limestone) in 20 °C water. As grain size ranges from 1 to 5 mm (a narrow band including 2 mm), sediment suspension becomes vanishingly small at normal flood conditions in alluvial rivers. We refer to this range as pea gravel. We further show that bedload movement of a clast in the pea gravel range, e.g. with a size of 4 mm moving over a bed of 0.4 mm particles has an enhanced relative mobility as compared to a clast with a size of 40 mm moving over a bed of the same 4 mm particles. With this in mind, we use 2 mm here as shorthand for the narrow pea gravel range of 1 – 5 mm, over which transport behaviour is distinct from both coarser and finer material. The use of viscosity allows delineation of a generalized dimensionless bed grain size discriminator between “sand-like” and “gravel-like” rivers that is applicable to sediment transport on Titan (ice clasts in flowing methane/ethane liquid at reduced gravity) and Mars (mafic clasts in flowing water at reduced gravity) as well as Earth.