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

Published online by Cambridge University Press:  01 June 2009

JORGE LORENZO-TRUEBA ,
VAUGHAN R. VOLLER ,
TETSUJI MUTO ,
WONSUCK KIM ,
CHRIS PAOLA  and
JOHN B. SWENSON
JORGE LORENZO-TRUEBA
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA
VAUGHAN R. VOLLER*
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA
TETSUJI MUTO
Affiliation:
Faculty of Environmental Studies, Nagasaki University, Nagasaki, Japan
WONSUCK KIM
Affiliation:
Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, TX 78712, USA
CHRIS PAOLA
Affiliation:
St. Anthony Falls Laboratory, Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55414, USA
JOHN B. SWENSON
Affiliation:
Department of Geological Sciences, University of Minnesota, Duluth, MN 55812, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 427 - 443
Copyright
Copyright © Cambridge University Press 2009

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