Can the growth of deltaic shorelines be unstable?

Abstract

Abstract. We study a sedimentary delta prograding over a fixed adversely sloping bathymetry, asking whether a perturbation to the advancing shoreline will grow (unstable) or decay (stable) through time. To start, we use a geometric model to identify the condition for acceleration of the shoreline advance (autoacceleration). We then model the growth of a delta on to a fixed adverse bathymetry, solving for the speed of the shoreline as a function of the water depth, foreset repose angle, fluvial topset slope, and shoreline curvature. Through a linearization of this model, we arrive at a stability criterion for a delta shoreline; indicating that autoacceleration is a required for an unstable growth. This is the first time such a shoreline instability has been identified and analyzed. We use the derived stability criterion to identify a characteristic lateral length-scale for the shoreline morphology resulting from an unstable growth. On considering example experimental and field conditions we observe that this length scale is typically larger than other geomorphic features in the system, e.g., channel spacings and dimensions, suggesting that the signal of the shoreline growth instability in the landscape might be shredded by other surface building processes, e.g., channel avulsions and along shore transport.

Morphodynamic Modeling of River-Dominated Deltas: A Review and Future Perspectives

“…2, the solution predicts a decelerating progradation rate as delta area grows and/or basin depth increases. But, delta progradation can accelerate, for instance, in "back-tilted" basins where the water depth shallows basinward Zhao et al, 2019).…”