Teasing out Simplicity from Complexity: the Law of Constant Bankfull Velocity in Alluvial Rivers

Abstract:

Of interest here are single-tread alluvial channels (or mildly anastomosing reaches with a single dominant channel) which are self-formed within their own floodplain. The 232 reaches considered here cover nearly the entire range of such channels, with bankfull discharge varying from 3.3x10^-1 m³/s to 2.6x10⁵ m³/s, characteristic bed material size varying from 0.04 mm to 168 mm, bed slopes varying from 8x7x10^-6 to 5.2x10^-2 and bankfull depths varying from 2.2x10^-1 m to 4.8x10¹ m. These channels show complexity at every scale, including the organization of bed grains, the existence or absence of bedforms such as dunes and bars, the state of eroding banks (e.g. fallen trees, rooted stumps, or slump blocks) and the species and density of floodplain vegetation. Scientific research can often be broadly classified into two types: a) research that shows that a system formerly thought to be relatively simple is instead much more complex, with an increase in the number of factors which must be considered to obtain understanding; and b) research which extracts general, broad-brush simplicity from complexity. Both approaches can contribute to the advancement of science. Here we consider the second approach. The problem in question pertains to an explanation of an observation from the time of Luna Leopold: the single bankfull parameter that appears to be invariant is bankfull flow velocity. Here we demonstrate this result empirically at first-order, obtaining the estimate of 1.5 m/s across scales. We then derive a single, universal dimensionless number that specifies bankfull velocity, again across scales. The result is independent of bed material grain size, suggesting that previously-ignored wash load plays a major, and perhaps the dominant role as floodplain material load in setting bankfull velocity.