Abstract

Exner's classical approach for the evolution of a bedform is applied to a cylindrical closed conduit. The discontinuity that appears in a progressive wave after a given time is overcome using an entropy solution. Exner's original equation is used to determine the bedload relation. This simple model reproduces the general features of bedforms inside closed conduits, while the numerical entropy solution is free of oscillations. This simplified analysis represents a first step towards developing a more complex model that considers the momentum equation including a frictional term.