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.

Coexistence of Two Dune Growth Mechanisms in a Landscape‐Scale Experiment

“…Over short timescales, the linear regime of this instability is responsible for the emergence of periodic dunes, assuming that all modes (wavelengths) grow exponentially independently from each other (Lü et al., 2021). Over longer timescales, a non‐linear regime of dune pattern coarsening dominated by collisions and interactions between bedforms leads to an increase in dune amplitude and wavelength in space and time (Gadal, Narteau, Ewing, et al., 2020; Gao, Narteau, & Rozier, 2015; Jarvis et al., 2022). In areas of limited sediment supply, dunes adopt crescentic shapes that can also elongate by depositing at their tips the sediment that is transported along their crests (Courrech du Pont et al., 2014; Fernandez‐Cascales et al., 2018; Gadal, Narteau, Courrech du Pont et al., 2020; Gao, Narteau, Rozier, & Courrech du Pont, 2015; Lü et al., 2017; Lucas et al., 2014; Lucas et al., 2015; Parteli et al., 2009; Reffet et al., 2010; Zhang et al., 2012).…”

The probabilistic nature of dune collisions in 2D

“…The inverse relationship between dune size and velocity means that faster, smaller dunes can approach and collide with slower, larger dunes. Such collisions have been frequently observed in subaqueous experiments and numerical simulations, and have been shown to play an important role in pattern coarsening, whereby a larger number of smaller dunes transition to become a smaller number of larger dunes (Coleman and Melville, 1994;Gao et al, 2015;Bradley and Venditti, 2019;Jarvis et al, 2022). This coarsening process primarily occurs through dune coalescence, where a pair of colliding dunes merge.…”

“…In these settings, dunes have long been thought to grow to attain a maximum height which, in settings with sufficient sediment, could be controlled by the flow depth (in aqueous environments) or the thickness of the planetary boundary layer (for aeolian systems) (Andreotti et al, 2009;Andreotti and Claudin, 2013). Alternatively, sediment supply may be an additional limiting factor (Gunn et al, 2022;Jarvis et al, 2022). Regardless, the migration velocity c of a dune depends inversely on the dune size.…”

“…Two distinct types of coalescence have been observed, downstream-and upstream-dominant, defined according to which peak survives the coalescence process (Coleman and Melville, 1994;Gao et al, 2015;Jarvis et al, 2022). Another possible collision outcome that has been recognized experimentally is ejection, where mass is transferred from the downstream larger, slower dune, to the upstream, smaller, faster dune, until the leading dune becomes sufficiently small that it can accelerate away (Diniega et al, 2010;Gao et al, 2015;Jarvis et al, 2022).…”

Coexistence of two dune growth mechanisms in a landscape-scale experiment

“…Over short timescales, the linear regime of this instability is responsible for the emergence of periodic dunes, assuming that all modes (wavelengths) grow exponentially independently from each other (Lü et al, 2021). Over longer timescales, a non-linear regime of dune pattern coarsening dominated by collisions and interactions between bedforms leads to an increase in dune amplitude and wavelength in space and time (Gadal, Narteau, Ewing, et al, 2020;Jarvis et al, 2022). In areas of limited sediment supply, dunes adopt crescentic shapes that can also elongate by depositing at their tips the sediment that is transported along their crests (Courrech du Pont et al, 2014;Fernandez-Cascales et al, 2018;Gadal, Narteau, Courrech du Pont et al, 2020;Gao, Narteau, Rozier, & Courrech du Pont, 2015;Lü et al, 2017;Lucas et al, 2014;Lucas et al, 2015;Parteli et al, 2009;Reffet et al, 2010;Zhang et al, 2012).…”