Theory for the curvature dependence of delta front progradation

Ke, Wun-Tao; Capart, Hervé

doi:10.1002/2015gl066455

Cited by 9 publications

(16 citation statements)

References 29 publications

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“…It is common for geometric delta models to impose a radially averaged foreset slope [ Swenson et al , ; Kim et al , ; Wolinsky , ; Mahon et al , ]. Results from the WLD (Figure b) show that this technique need not be limited to geometric studies, but an appropriate slope could be imposed in increasingly complex, channel‐resolving models if the flow field outside of the delta is resolved [e.g., Ke and Capart , ]. This approach could improve our understanding of river delta morphodynamics by eliminating unnecessary complexity in future modeling studies.…”

Section: Discussionmentioning

confidence: 99%

Flow patterns and morphology of a prograding river delta

2016

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The transition of flow between laterally confined channels and the unchannelized delta front controls the morphodynamic evolution of river deltas but has rarely been measured at the field scale. We quantify flow patterns and bathymetry that define the evolution of the subaqueous delta front on the Wax Lake Delta, a rapidly prograding delta in coastal Louisiana. A significant portion of flow (∼59%) departs the channel network over lateral channel margins as opposed to the downstream channel tips. Bathymetric surveys and remotely sensed estimates of flow direction allow spatial changes in flow velocity to be quantified and patterns of erosion and deposition to be estimated. Shallowing along channel margins produces spatial acceleration and erosion. Lateral spreading, deceleration, and deposition occur within three to eight channel widths outside of the channel margins. In interdistributary bays, the shape of each flow path is constrained by "nourishment boundaries" that separate the outflows from neighboring channels. Deposit elevation decreases with a basinward slope of 2.4 × 10 −4 with distance from a channel margin along any flow path, regardless of the channel or location that flow departed the network. Bathymetric depressions called "interdistributary troughs" form along nourishment boundaries where flow paths are the longest and deposit elevation is correspondingly low. We conclude that the deposit morphology exerts a strong control on bathymetric evolution and that interaction between neighboring channels and even neighboring deltas can influence delta front morphology.

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Section: Discussionmentioning

confidence: 99%

Flow patterns and morphology of a prograding river delta

2016

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“…We construct a model to describe the evolution of this boundary. Moving boundary models have been successfully used to explore delta shoreline evolution by decomposing deltas into the domains landward and seaward of a shoreline, neglecting channels (Ke & Capart, ; Lorenzo‐Trueba et al, ; Swenson et al, ; Wolinsky, ). We will model the channel network with this approach for the first time and name the model MB_DCN for Moving Boundary of a Distributary Channel Network.…”

Section: Moving Boundary Model For Distributary Channel Network: Mb_dcnmentioning

confidence: 99%

Distributary Channel Networks as Moving Boundaries: Causes and Morphodynamic Effects

Shaw

Mahon

et al. 2019

JGR Earth Surface

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We propose an exploratory model to describe the morphodynamics of distributary channel network growth on river deltas. The interface between deep channels and the shallow, unchannelized delta front deposits is modeled as a moving boundary. Steady flow over the unchannelized delta front is friction dominated and modeled by Laplace's equation. Shear stress along the network boundary produces nonlinear erosion rates at the interface, causing the boundary to move and network elements (channels and branches) to form. The model was run for boundary conditions resembling the Wax Lake Delta in coastal Louisiana, 20 parameterizations of sediment transport, and 3 parameterizations of discharge. In each case, the model produced a complex channel network with channel number, width, bifurcation angle, and channel shape depending on the sediment transport formula. For reasonable sediment transport parameters and gradually increasing water discharge, the model produced network characteristics and progradation rates similar to the Wax Lake Delta. This suggests that the model contains the processes responsible for network growth, despite its abstract formulation. Key Points:• Prograding distributary channel networks of varying morphology can be modeled as a simple moving boundary • Nonlinearities in the sediment transport formula dictate channel width, number of branches, bifurcation angle, and channel shape • Evolution is dictated by network morphology, sediment transport, and water discharge Supporting Information:• Supporting Information S1

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“…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). This analogy is based on the construction of a shoreline mass balance condition, equating the sediment flux arriving to the rate of its advance -a condition directly analogous to the phase change interface heat balance Stefan condition in melting problems (Crank, 1984).…”

Section: Introductionmentioning

confidence: 99%

“…This analogy is based on the construction of a shoreline mass balance condition, equating the sediment flux arriving to the rate of its advance -a condition directly analogous to the phase change interface heat balance Stefan condition in melting problems (Crank, 1984). The original shore balance proposed by Swenson et al (2000) has been recently modified by Ke and Capart (2015) to account for the shoreline planform curvature. Recognizing the extensive work related to the role of curvature in the morphological instability of growing interfaces (Mullins and Sekerka, 1963;Sekerka et al, 2014;Paterson, 1981;Li et al, 2004Li et al, , 2009Zhao et al, 2016), this modification allows us to expand the so-called Swenson-Stefan analogy to develop a criterion for an unstable delta shoreline advance.…”

Section: Introductionmentioning

confidence: 99%

“…To set the stage for our study, we adopt the delta geometry used in the López et al (2014) model, and then, on invoking the additional simplifying assumption of a static basin with a constant water level, we arrive at an explicit criterion for the onset of auto-acceleration. 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.…”

Section: Introductionmentioning

confidence: 99%

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Can the growth of deltaic shorelines be unstable?

Zhao

Salter

Voller³

et al. 2019

Earth Surf. Dynam.

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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.

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Theory for the curvature dependence of delta front progradation

Cited by 9 publications

References 29 publications

Flow patterns and morphology of a prograding river delta

Flow patterns and morphology of a prograding river delta

Distributary Channel Networks as Moving Boundaries: Causes and Morphodynamic Effects

Can the growth of deltaic shorelines be unstable?

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