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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/esurf-2018-87
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-2018-87
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 18 Jan 2019

Research article | 18 Jan 2019

Review status
This discussion paper is a preprint. A revision of the manuscript is under review for the journal Earth Surface Dynamics (ESurf).

Can the growth of deltaic shorelines be unstable?

Meng Zhao1, Gerard Salter2, Vaughan R. Voller3, and Shuwang Li4 Meng Zhao et al.
  • 1Department of Mathematics, University of California, Irvine, CA 92697, USA
  • 2Department of Earth Sciences, University of Minnesota, Minneapolis, MN 55455, USA
  • 3Department of Civil, Environmental, and Geo-Engineering, St. Anthony Falls Laboratory, 500 Pillsbury Drive SE, Minneapolis, MN 55455, USA
  • 4Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA

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.

Meng Zhao et al.
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Meng Zhao et al.
Meng Zhao et al.
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Latest update: 24 Apr 2019
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Short summary
Typically we think of a shoreline growing with a smooth line separating the land and the water. If the growth is unstable, however, the land/water front would exhibit a roughness that grows with time. Here we ask, Can the growth of deltaic shorelines be unstable? Through mathematical analysis we show that growth is unstable when the shoreline is building on to an adverse slope. The length scale of the unstable signal in such a case, however, might be obscured by other geomorphic processes.
Typically we think of a shoreline growing with a smooth line separating the land and the water....
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