A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change

Jorge Lorenzo Trueba, Vaughan R. Voller, Chris Paola

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.

Original languageEnglish
Pages (from-to)39-47
Number of pages9
JournalComputers and Geosciences
Volume53
DOIs
StatePublished - 1 Apr 2013

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shoreline
bedrock
mathematics
prediction
Nonlinear equations
Ordinary differential equations
mass balance
Gravitation
Sediments
Dynamical systems
cross section
Rivers
gravity
Testing
river
sediment
experiment
Experiments

Keywords

  • Alluvial-bedrock transition
  • Fluvially dominated
  • Moving boundary
  • Shoreline dynamics

Cite this

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title = "A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change",
abstract = "We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.",
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A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change. / Lorenzo Trueba, Jorge; Voller, Vaughan R.; Paola, Chris.

In: Computers and Geosciences, Vol. 53, 01.04.2013, p. 39-47.

Research output: Contribution to journalArticleResearchpeer-review

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AB - We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.

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