×

A similarity solution for a dual moving boundary problem associated with a coastal-plain depositional system. (English) Zbl 1181.76114

Summary: 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.

MSC:

76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ponce, Engineering Hydrology, Principles and Practices (1989)
[2] Posamentier, AAPG Bull. 76 pp 1687– (1992)
[3] DOI: 10.1061/(ASCE)0733-9429(1998)124:10(985) · doi:10.1061/(ASCE)0733-9429(1998)124:10(985)
[4] Parker, Proceedings of the Third IAHR Symposium, River, Coastal and Estuarine Morphodynamics pp 558– (2003)
[5] DOI: 10.1017/S0022112078002505 · Zbl 0398.76011 · doi:10.1017/S0022112078002505
[6] Meyer-Peter, Second Meeting of the Intl Association for Hydraulic Structures Research (1948)
[7] DOI: 10.1029/2004JF000274 · doi:10.1029/2004JF000274
[8] DOI: 10.1046/j.1365-2117.2000.00134.x · doi:10.1046/j.1365-2117.2000.00134.x
[9] Paola, Basin Res. 4 pp 73– (1992) · doi:10.1111/j.1365-2117.1992.tb00145.x
[10] DOI: 10.1029/2006JF000617 · doi:10.1029/2006JF000617
[11] DOI: 10.1130/G21923.1 · doi:10.1130/G21923.1
[12] DOI: 10.1029/2006JF000561 · doi:10.1029/2006JF000561
[13] DOI: 10.1029/2005JF000284 · doi:10.1029/2005JF000284
[14] Dade, J. Geol. 106 pp 661– (1998)
[15] DOI: 10.1016/j.jcp.2004.11.039 · Zbl 1121.76373 · doi:10.1016/j.jcp.2004.11.039
[16] Crowell, Evolution of Ridge Basin, Southern California: An Interplay of Sedimentation and Tectonics (2003)
[17] Crank, Free and Moving Boundary Problems (1984)
[18] DOI: 10.2110/jsr.2007.009 · doi:10.2110/jsr.2007.009
[19] Anderson, Late Quaternary Stratigraphic Evolution of the Northern Gulf of Mexico Margin (2004) · doi:10.2110/pec.04.79
[20] DOI: 10.1017/S0022112086002938 · Zbl 0599.76125 · doi:10.1017/S0022112086002938
[21] DOI: 10.1016/j.ijheatmasstransfer.2004.07.007 · Zbl 1077.80004 · doi:10.1016/j.ijheatmasstransfer.2004.07.007
[22] DOI: 10.1108/09615530610669157 · Zbl 1121.86006 · doi:10.1108/09615530610669157
[23] DOI: 10.1016/S0017-9310(96)00330-4 · Zbl 0921.76175 · doi:10.1016/S0017-9310(96)00330-4
[24] DOI: 10.1017/S0956792500004198 · Zbl 0964.80005 · doi:10.1017/S0956792500004198
[25] DOI: 10.1111/j.1365-3091.2006.00830.x · doi:10.1111/j.1365-3091.2006.00830.x
[26] Sommerfield, Continental-Margin Sedimentation: Transport to Sequence Stratigraphy (2007)
[27] DOI: 10.1029/2006JF000549 · doi:10.1029/2006JF000549
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.