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 (auto-acceleration). 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 top set slope, and shoreline curvature. Through a linearization of this model, we arrive at a stability criterion for a delta shoreline, indicating that auto-acceleration is a necessary condition for 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 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 alongshore transport.
Highlights
Shorelines are the moving boundary between land and sea, and their evolution is of great importance to the estimated 10% of the global population that live in their proximity (Wong et al, 2014)
On noting the strictly nonnegative nature of most of the terms in this expression, it follows that for an unstable growth – an increase in the perturbation amplitude with time – the numerator in the bracket term on the right hand needs to be negative, i.e., the condition for unstable shoreline growth is. This criterion states that unstable growth requires the presence of an adverse effective basement slope SBe < 0; i.e., the auto-acceleration condition in Eq (3) is a necessary condition for unstable shoreline growth
To provide a physical context that enables us to analyze our stability criterion under conditions that are consistent with realizable experimental systems, we consider the XES10 experiment reported in Hajek et al (2014), an experiment designed to study the growth of shoreline in the presence of a back-tilted subsidence
Summary
Shorelines are the moving boundary between land and sea, and their evolution is of great importance to the estimated 10% of the global population that live in their proximity (Wong et al, 2014). In a one-dimensional modeling and experimental study, López et al (2014) indicated that, for some combinations of sediment input and subsidence style, delta progradation on an adverse slope could exhibit a positive acceleration, referred to as “auto-acceleration” We think that such a behavior could be a critical ingredient for the onset of unstable growth. In exploring the possible instability associated with autoacceleration, we will appeal to the analogy between solid and liquid phase change processes and delta shoreline advance (Swenson et al, 2000; Voller et al, 2004; Capart et al, 2007; Lorenzo-Trueba et al, 2009; Voller, 2010; Ke and Capart, 2015; Lai et al, 2017). To see and understand how such a condition may lead to an unstable growth condition, we further perform a linear stability analysis of the Ke and Capart (2015) shoreline condition, identifying the criterion when a specified small perturbation on a planar autoaccelerating shoreline front would be expected to grow, i.e., become unstable
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