River deltas are a compelling target for numerical simulation because they contain seemingly organized patterns and shapes at a variety of scales. For instance, most river-dominated deltas, regardless of size, have triangular to semi-circular planform shapes, channel networks, and channel bifurcations. The common presence of these features among most deltas in the world (Caldwell et al., 2019; Nienhuis et al., 2020) suggests there are consistent underlying physical processes controlling delta form and behavior. In this review, we discuss how numerical modeling, and more specifically a type of modeling focused on the morphodynamic feedback, has helped explore some of these key physical processes over the last 15 years.

Some aspects of the dynamics of aeolian transport over a flat sediment bed have been thoroughly investigated and are relatively well understood. The interactions between grains in transport and the wind give rise to well-known dynamical scaling laws for the fluxes and concentrations of grains in most of the transport layer. However, recent work has revealed a sudden shift in these scaling laws near the granular surface and below. While the vertical flux of grains in the transport layer scale linearly with excess wind shear stress, the vertical flux near the granular surface—the ‘erosion rate’—scales linearly with wind speed. Analysis of numerical modeling results reveal that near-surface horizontal and vertical fluxes are important for the instability that leads to wind ripple growth and stabilization as well as ripple propagation. A few main open questions are: What are the physical mechanisms behind the scaling of the erosion rate with wind speed? Could they arise from the small subpopulation of high-energy grains, who’s characteristics scale differently than the average grain in transport? As these grains move downward from the free-wind layer, do they tend to retain their properties as they pass through the feedback layer, delivering their energy, momentum and scaling directly to the bed? Do collisions between grains near and within the bed, which redistribute energy and momentum from high-energy impacts, play a key role in determining the scaling of near-bed fluxes? How important are potential collective effects that can occur when impacts with sufficient energy to excite the bed occur close together in time and space? An answer to these questions would help complete our understanding of the physics of aeolian transport, with repercussions that shed light onto the emergence and propagation of wind ripples. Using a detailed grain scale numerical model, we are investigating the dynamics of grains near the granular bed, and what saltation properties drive these dynamics. Preliminary results, including velocity distributions near the bed, indicate that the signal from high-energy grains that traverse the feedback layer from above reaches the bed surface, consistent with the hypothesis that the surface erosion rate is related to this small population of grains who’s characteristics scale with the free-wind speed.

The dynamics and evolution of deltas and their channel networks involve interactions between many factors, including water and sediment discharge and cohesion from fine sediment and vegetation. These interactions are likely to affect how much vegetation influences deltas, because increasing sediment discharge increases aggradation rates on the delta and may result in sediment transport processes happening on timescales that are faster than those for vegetation growth. We explore how varying water and sediment discharge changes vegetation’s effect on delta evolution. We propose two new insights into delta evolution under different discharge conditions. First, without vegetation, we observe a regime shift in avulsion dynamics with increasing water discharge, from a few active channels supplemented by overbank flow and undergoing episodic avulsion (with low discharge) to many active channels experiencing frequent partial avulsions (with high discharge). Second, with vegetation, increased aggradation results in more frequent switching of the dominant channels with increased sediment discharge, but also prevents vegetation from establishing in non-dominant channels resulting in more frequent channel reoccupation and therefore greater stability in channel network planform. These insights have important implications for understanding the distribution of water, sediment, and nutrients on deltas in the face of future changes in climate, human modifications of fluxes of sediment and water to the coast, and especially for restored or engineered deltas with controlled water or sediment discharges.