Sediment Convection‐Diffusion and Bedform Length

Abstract

In connection with the mechanics of ripples and dunes, the governing equations of convection‐diffusion of suspended sediment in two‐dimensional flow fields over ripples or dunes are solved by the finite‐element method. The role of suspended sediment in determining the steady bedform length is theoretically investigated. The postulate that, in the case of steady bedforms, the diffusive flux vector at any point on the stoss must point into the interior of the flow region divides mathematically acceptable solutions into two categories: (1) Physically acceptable solutions; and (2) physically unacceptable solutions. The marginal solutions, which lie on the common boundary between the two classes in the solution space, are of special interest. They represent steady bedforms with minimum length under the prevailing flow conditions, and they are conjectured to correspond to the steady bedforms occurring in nature. Finally, the theory is compared with the physical observations made in flumes, canals, and rivers. The comparison shows a fair agreement.