Transport of solids by natural water flow: evidence for a worldwide correlation

Abstract

The limited scope of laboratory experiments had suggested that at the same applied stream power, defined as bed shear stress multiplied by mean flow velocity, the unit mass transport rate of sand, as bedload, varies as (stream depth)$^{-\frac-{2}{3}}$ and as (grain size)$^{-\frac{1}{2}}$. Further, at constant flow depth the rate varies as (stream power)$^\frac{3}{2}$. To test the generality of these empirical relations they were used in reverse to convert measured transport rates in both natural rivers and small laboratory flumes to notional values corresponding to a common arbitrary flow depth and grain size. Plotting stream power against the converted transport rates, all the results fall along a single narrow belt extending over virtually the whole range of magnitude and grain size conditions found on Earth, irrespective of geology, climate, channel magnitude, irregularity and boundary roughness. No quantitative explanation of this correlation is apparent, but some qualitative ideas are suggested.