Dimensionless Illustration: The Grain Size 2 mm Is Indeed “Special” in the Context of Fluvial Sediment Transport and Morphology

Long rivers extending from the mountains to the sea often undergo a transition from gravel-bed to sand-bed. The grain size dividing “gravel” and “sand”, i.e. 2 mm, has, on an empirical basis, played a special role in fluvial sediment transport and morphology. Sand-bed rivers and gravel-bed rivers have traditionally been treated separately in terms of morphology and sediment transport. For example, the sediment transport relation of Wilcock and Crowe (2003) treats gravel transport as a function of sand content in the bed. While sand is easily suspended in rivers, there are only sparse records of gravel traveling in suspension under purely fluvial conditions (as opposed to debris flows), and these records become vanishing as grain size increases. Here we study the reason for this in terms of sediment entrainment into suspension from the bed. Garcia and Parker (1991) developed a relation for the rate of suspension of sand from an alluvial, non-cohesive bed. This relation was developed exclusively based on empirical data for sand beds. When the relation is extrapolated to gravel beds, it is found to predict copious suspension where there should be none. The key parameter controlling this is a particle Reynolds number, Re_p = (RgD)^1/2D/n, where D is grain size, n is fluid kinematic viscosity, R is particle submerged specific gravity and g is gravitational acceleration. However, in the case of spheres, there is a unique relation between particle Reynolds number and dimensionless fall velocity R_f = v_s/(RgD)^1/2. The Garcia-Parker relation can easily be cast in terms of R_f rather than R_ep over the range of sand grain sizes used in the derivation. The curve of R_f versus R_ep, however, shows a monotonically increasing zone for small R_ep but an approximate plateau region for larger values of R_ep. The transitional range between the monotonically increasing and plateau region is R_ep = 360 to 600. In the case of quartz in 20° water on Earth, this corresponds to the range 2.0 – 2.8 mm. In the plateau region, the modified Garcia-Parker relation is found to predict negligible suspension of sediment (gravel) within the range of shear velocities most commonly found in rivers. Suspension of gravel is not in principle precluded by the relation, but the conditions commonly found on Earth during floods, even megafloods, do not seem to allow it (Larsen and Lamb, 2016). The result is further verified using the relation for entrainment into suspension by deLeeuw et al. (2020). The results have significance for the interpretation of such phenomena as downstream fining in rivers and gravel-sand transitions. The dimensionless form of the result allows for straightforward modification to the case of ice clasts in liquid methane at the gravitational acceleration.