Mathematical Modeling of Shoreline Evolution

Mahaute, Bernard Le; Soldate, Mills

doi:10.9753/icce.v16.67

Cited by 7 publications

(3 citation statements)

References 1 publication

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“…Our modeling goal is not to simulate any one location in fine detail, but to study the types of shoreline behavior that can arise from the basic instability in shoreline shape. Extending the concepts of other common one‐line models used in many coastal studies [ LeMehaute and Soldate , 1977; Ozasa and Brampton , 1980; Hanson and Kraus , 1989], this model contains a new, numerically stable solution scheme to treat the case of high‐angle waves. As suggested by the simple analysis above, the high‐angle instability should lead to offshore‐extending spits which present unique challenges to a line‐based model; our model accommodates a shoreline that becomes arbitrarily sinuous, even doubling back on itself.…”

Section: Numerical Modelmentioning

confidence: 99%

High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

2006

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[1] Contrary to traditional findings, the deepwater angle of wave approach strongly affects plan view coastal evolution, giving rise to an antidiffusional ''high wave angle'' instability for sufficiently oblique deepwater waves (with angles between wave crests and the shoreline trend larger than the value that maximizes alongshore sediment transport, $45°). A one-contour-line numerical model shows that a predominance of high-angle waves can cause a shoreline to self-organize into regular, quasiperiodic shapes similar to those found along many natural coasts at scales ranging from kilometers to hundreds of kilometers. The numerical model has been updated from a previous version to include a formulation for the widening of an overly thin barrier by the process of barrier overwash, which is assumed to maintain a minimum barrier width. Systematic analysis shows that the wave climate determines the form of coastal response. For nearly symmetric wave climates (small net alongshore sediment transport), cuspate coasts develop that exhibit increasing relative cross-shore amplitude and pointier tips as the proportion of high-angle waves is increased. For asymmetrical wave climates, shoreline features migrate in the downdrift direction, either as subtle alongshore sand waves or as offshore-extending ''flying spits,'' depending on the proportion of high-angle waves. Numerical analyses further show that the rate that the alongshore scale of model features increases through merging follows a diffusional temporal scale over several orders of magnitude, a rate that is insensitive to the proportion of high-angle waves. The proportion of high-angle waves determines the offshore versus alongshore aspect ratio of selforganized shoreline undulations.

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Section: Numerical Modelmentioning

confidence: 99%

High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

2006

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“…Pelnard-Considere (1956) is attributed with describing the first quantitative shoreline-change model (see LeMehaute and Soldate, 1977). This type of model is called a One-Line model hecause it tracks the position of one contour line, usually the shoreline, over time.…”

Section: The One-line Modelmentioning

confidence: 99%

“…Using these assumptions and the sediment transport equation shown above, an analytical solution can be obtained (Larson and Kraus, 1991;LeMehaute and Soldate, 1977). The analytical solution (with the small wave angle assumption) allows for the angle of wave breaking to be defined as function of the local shoreline orientation because this is altered by the placement of the fill (see Dean, 2002).…”

Section: The One-line Modelmentioning

confidence: 99%

Evaluation of Beach Nourishment Evolution Models Using Data from Two South Carolina, USA Beaches: Folly Beach and Hunting Island

Weathers

Voulgaris²

2013

Journal of Coastal Research

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Beach nourishment is a common method used for mitigating coastal erosion. However, it is also a costly undertaking and requires an appropriate cost-to-benefit analysis. Althougb the costs can be estimated relatively easily, the benefits are directly related to tbe life expectancy of the proposed project. With tbis in mind, tbree existing beach replenishment time-evolution models (the Linear Erosion, the Verhagen, and the One-Line models) were compared for their ability to represent data from two beacb nourishment projects that have taken place in South Carolina, USA, at Folly Beach and Hunting Island. Another newly introduced model that combines the One-Line model with elements of the Verhagen model was also tested against the data from the beach nourishment projects. In addition to hindcast evaluation, the four models were employed to predict beach fill evolution at hoth locations, and those results were compared using the existing fill evolution data. Although all models provided a satisfactory statistical fit, the fitted parameter values from the Linear Erosion, the Verhagen, and the combined models failed to adequately describe physical processes associated with the development of each model. On the other hand, the One-Line model was able to describe beach fill volume evolution at botb locations. The discrepancy between the models was exemplified in their application without the henefit of the statistical fitting. Overall, it was found that the One-Line model represented a more versatile approach to predicting volume losses hecause it is based on physical concepts of wave-induced sediment transport, and as such, it was better suited for use at any location as long as accurate information about tbe wave climate is available. Furthermore, detailed investigation at each site indicated that hoth the role of barrier island processes and the role of inlet dynamics in the evolution of heaches and beach fill were not fully recognized by the models and should be considered in tbe cost-henefit analysis of heacb nourishment projects at barrier islands adjacent to ebb tidal deltas.

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Erosion at Bend of Gravel Causeway Due to Waves

Kobayashi¹,

Han²

1988

J. Waterway, Port, Coastal, Ocean Eng.

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Mathematical Modeling of Shoreline Evolution

Cited by 7 publications

References 1 publication

High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

Evaluation of Beach Nourishment Evolution Models Using Data from Two South Carolina, USA Beaches: Folly Beach and Hunting Island

Erosion at Bend of Gravel Causeway Due to Waves

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