Selective Sorting and Abrasion of River Gravel. I: Theory

Abstract

Most gravel rivers show a tendency for characteristic grain size to decrease in the downstream direction over scales of tens or hundreds of kilometers. It has been surmised that this downstream fining is due to some combination of selective sorting, by which finer grains are preferentially transported downstream; and abrasion, by which individual particles are reduced in size. Here a framework for the simultaneous treatment of both phenomena is developed. The analysis is restricted to bed‐load transport of gravel. Only abrasion due to binary collisions between moving bed load and stationary bed particles is considered. The formulation includes the possibility of differential basin uplift and subsidence due to tectonism, and mixtures of rock types with differing coefficients of abrasion. The formulation of selective sorting is based on the concept of hiding, as applied to a surface‐based bed‐load transport relation. Abrasion is first treated in terms of a Lagrangian formulation for individual grains, and then transformed into an Eulerian expression that appears in the formulation of gravel mass balance.