Bed and flow dynamics leading to sediment‐wave initiation

Abstract

New PIV‐based experiments show that the nascent seed waves from which both ripples and dunes develop are generated on planar mobile sediment beds in a two‐stage process. The first stage comprises the motion of random sediment patches that reflect the passage of sediment‐transport events caused by attached eddies. These eddy‐transport events propagate at speeds that are proportional to their size and less than overhead eddy convection velocities, but potentially larger than local average fluid and sediment velocities. In the second stage, interactions of the moving patches result in a bed disturbance that exceeds a critical height and interrupts the bed‐load layer. Quasi‐regular seed waves are then generated successively downstream of this stabilised growing disturbance via a scour‐deposition wave that arises from the requirement of sediment mass conservation and the sediment‐transport and bed‐stress distributions downstream of a bed perturbation. Seed waves are thereby of preferred lengths that scale with the grain size, i.e. length = O(130) grain diameters, agreeing with compiled measurements. This two‐stage generation mechanism is valid for fully‐turbulent hydraulically‐smooth and rough‐bed flows of small to large sediment transport rates. It is furthermore valid for laminar flows, although the critical disturbances leading to seed‐wave generation arise through bed discontinuities, and not eddy‐based sediment‐transport events. The identified generation mechanism, which accounts for turbulence effects, explains the observed similar scaling of alluvial, closed‐conduit and lightweight‐sediment seed waves. The present measurements highlight further aspects of the flow dynamics preceding seed‐wave generation, including: decreases in von Kármán's constant due to bed mobility, near‐bed eddy convection speeds in excess of local double‐averaged (in time and space) streamwise velocities, and the validity of the four‐range spectral scaling model for open‐channel flows proposed earlier by Nikora.