A similarity solution for a dual moving boundary problem associated with a coastal-plain depositional system

Jorge Lorenzo-Trueba, Vaughan R. Voller, Tetsuji Muto, Wonsuck Kim, Chris Paola, John B. Swenson

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31 Citations (Scopus)


Assuming that the sediment flux in the Exner equation can be linearly related to the local bed slope, we establish a one-dimensional model for the bed-load transport of sediment in a coastal-plain depositional system, such as a delta and a continental margin. The domain of this model is defined by two moving boundaries: the shoreline and the alluvial-bedrock transition. These boundaries represent fundamental transitions in surface morphology and sediment transport regime, and their trajectories in time and space define the evolution of the shape of the sedimentary prism. Under the assumptions of fixed bedrock slope and sea level the model admits a closed-form similarity solution for the movements of these boundaries. A mapping of the solution space, relevant to field scales, shows two domains controlled by the relative slopes of the bedrock and fluvial surface: one in which changes in environmental parameters are mainly recorded in the upstream boundary and another in which these changes are mainly recorded in the shoreline. We also find good agreement between the analytical solution and laboratory flume experiments for the movements of the alluvial-bedrock transition and the shoreline.

Original languageEnglish
Pages (from-to)427-443
Number of pages17
JournalJournal of Fluid Mechanics
Publication statusPublished - 2009

Bibliographical note

Funding Information:
This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under the agreement number EAR-0120914. The authors would also like to thank Kyle Straub for discussions related to the values of the alluvial–bedrock slope ratio in the stratigraphy of the Gulf of Mexico.

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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