Coarsening Dynamics of 2D Subaqueous Dunes

Abstract : Fluid flow over an initially flat granular bed leads to the formation of a surface-wave instability. The sediment bed profile coarsens and increases in amplitude and wavelength as disturbances develop from ripples into dunes. We perform experiments and numerical simulations to quantify both the temporal evolution of bed properties and the relationship between the initial growth rate and the friction velocity u_∗. Experimentally, we study underwater bedforms originating from a thin horizontal particle layer in a narrow and counter-rotating annular flume. We investigate the role of flow speed, flow depth and initial bed thickness on dune evolution. Bedforms evolve from small, irregular disturbances on the bed surface to rapidly growing connected terraces (2D equivalent of transverse dunes) before splitting into discrete dunes. Throughout much of this process, growth is controlled by dune collisions which are observed to result in either coalescence or ejection (mass exchange). We quantify the coarsening process by tracking the temporal evolution of the bed amplitude and wavelength. Additionally, we perform Large Eddy Simulations (LES) of the fluid flow inside the flume to relate the experimental conditions to u_∗. By combining the experimental observations with the LES results, we find that the initial dune growth rate scales approximately as u∗5 ${u}_\ast ⁵$. These results can motivate models of finite-amplitude dune growth from thin sediment layers that are important in both natural and industrial settings.