Journal of Fluid Mechanics

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

JORGE LORENZO-TRUEBAa1, VAUGHAN R. VOLLERa1 c1, TETSUJI MUTOa2, WONSUCK KIMa3, CHRIS PAOLAa4 and JOHN B. SWENSONa5

a1 St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA

a2 Faculty of Environmental Studies, Nagasaki University, Nagasaki, Japan

a3 Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, TX 78712, USA

a4 St. Anthony Falls Laboratory, Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN 55414, USA

a5 Department of Geological Sciences, University of Minnesota, Duluth, MN 55812, USA

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.

(Received August 22 2008)

(Revised February 20 2009)

Correspondence:

c1 Email address for correspondence: volle001@umn.edu

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