Sandy Spits and Their Mathematical Modeling

Abstract

AbstractA mathematical model of spit growth was derived based on the sand conservation equation, where the boundary fluxes of sand were specified as input and specific assumptions were made about the cross-sectional shape of the evolving sandy barrier. Analytical solutions were developed to the governing equation to primarily simulate spit elongation under unrestricted and restricted growth, although the time evolution of the spit cross-sectional area was also described for some cases. The solutions were validated with data from the field and the laboratory, including field data on unrestricted spit growth from Sweden and United States, and laboratory data on restricted spit growth from the Coastal and Hydraulics Laboratory in the United States. The laboratory data allowed for validating analytical solutions of spit growth involving varying spit cross-sectional area and active profile height, as well as the effect of sand transport through an inlet that erodes the tip of the spit. Two field cases constituting more complex sand transport conditions at inlets, where different morphological features interacted with the spit evolution, were also investigated, but numerical approaches were employed to solve the governing equations. These two cases included spit growth at Fire Island Inlet on Long Island in the United States, and at Chilaw Inlet in Sri Lanka. Overall, the mathematical model of spit growth reproduced the data well, although some calibration of relevant parameters and coefficients were typically needed.KeywordsSediment TransportRiver MouthSand TransportMorphological UnitLongshore Sediment TransportThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.