Abstract
A 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allard J, Bertin X, Chaumillon E, Pouget F (2008) Sand spit rhythmic development: a potential record of wave climate variations? Arçay Spit, western coast of France. Mar Geol 253:107–131
Angelbratt A, Kluft J (2007) Seasonal closure of Chilaw Inlet in Sri Lanka: physical processes and mathematical modeling. Unpublished M.S. report, Department of Water Resources Engineering, Lund University, Lund
Baranasuriya PW (2001) Hydrographic investigations for the design of an anchorage in a complex lagoon estuary: a spatial Odyssey. In: Proceedings of 42nd Australian Surveyors Congress, pp 1–12
Blomgren S, Hanson H (2000) Coastal geomorphology at the Falsterbo Peninsula, southern Sweden. J Coast Res 16(1):15–25
Camenen B, Larson M (2005) A bedload sediment transport formula for the nearshore. Estuar Coast Shelf Sci 63:249–260
Dean RG (1977) Equilibrium beach profiles: U.S. Atlantic and Gulf coasts. Ocean engineering technical report no. 12. Department of Civil Engineering and College of Marine Studies, University of Delaware, Newark
Evans OF (1942) The origin of spits, bars and related structures. J Geol 50:846–865
FitzGerald DM (1988) Shoreline erosional-depositional processes associated with tidal inlets. In: Aubrey DG, Weishar L (eds) Hydrodynamics and sediment dynamics of tidal inlets. Springer, Berlin, pp 186–225
FitzGerald DM, Kraus NC, Hands EB (2000) Natural mechanisms of sediment bypassing at tidal inlets. CHETN-IV-30. Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center, Vicksburg
Hallermeier RJ (1981) A profile zonation for seasonal sand beaches from wave climate. Coast Eng 4:253–277
Hanson H, Larson M (1993) Sand transport and coastal development at Skanör-Falsterbo. Report no. 3166, Department of water Resources engineering, Lund Institute of Technology, Lund University, Lund, Sweden (in Swedish)
Hoan LX, Hanson H, Larson M, Kato S (2011) A mathematical model of spit growth and barrier elongation: application to FireIsland Inlet (USA) and Badreveln Spit (Sweden). Estuar Coast Shelf Sci 93:468–477
Johnson DW (1919) Shore processes and shoreline development. Wiley, New York
Kana TW (1995) A mesoscale sediment budge for long island, New York. Mar Geol 126(1):87–110
Kieslich JM, Brunt DH (1989) Assessment of a two-layer beach fill at Corpus Christi Beach, TX. In: Proceedings of coastal zone 89, ASCE, New York, pp 3975–3984
Kraus NC (1998) Inlet cross-sectional area calculated by process-based model. In: Proceedings of 26th coastal engineering conference, ASCE, pp 3265–3278
Kraus NC (1999) Analytical model of spit evolution at inlets. In: Proceedings of coastal sediments 99, ASCE, Charleston, pp 1739–1754
Kraus NC (2000) Reservoir model of ebb-tidal shoal evolution and sand bypassing. J Waterw Port Coast Ocean Eng 126(6):305–313
Kraus NC, Lin L (2002) Coastal processes study of San Bernard River mouth Texas: stability and maintenance of mouth. Technical report TR-02-10. Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center, Vicksburg
Kraus NC, Seabergh WC (2002) Inlet spits and maintenance of navigation channels. CHETN-IV-44. Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center, Vicksburg
Larson M, Hanson H (2013) Coastal erosion and protection in Sweden. In: Pranzini E, Williams AT (eds) Coastal erosion and protection in Europe. Earthscan Ltd, Routledge, Oxon, pp 31–46
Larson M, Rosati JD, Kraus NC (2002a) Overview of regional coastal sediment processes and controls. CHETN-XIV-4. Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center, Vicksburg
Larson M, Kraus NC, Hanson H (2002b) Simulation of regional longshore sediment transport and coastal evolution – The Cascade model. In: Proceedings of 28th coastal engineering conference, ASCE, Wales, pp 2612–2624
Larson M, Erikson L, Hanson H (2004) An analytical model to predict dune erosion due to wave impact. Coast Eng 51:675–696
Larson M, Kraus NC, Connell KJ (2006) Modeling sediment storage and transfer for simulating regional coastal evolution. In: Proceedings of 30th coastal engineering conference, World Scientific, pp 3924–3936
Larson M, Wikramanayake N, Hanson H, Ranasinghe R (2009) Seasonal closure of Chilaw Inlet, Sri Lanka: physical processes and mathematical modeling. In: Proceedings of coastal dynamics 09, ASCE (on CD)
Larson M, Hanson H, Kraus NC, Hoan LX (2011) Analytical model for the evolution of coastal inlet cross-sectional area. In: Proceedings of coastal sediments 11, ASCE (on CD)
Otvos EG (2012) Coastal barriers – nomenclature, processes, and classification issues. Geomorphology 139–140:39–52
Petersen D, Deigaard R, Fredsoe J (2008) Modelling the morphology of sandy spits. Coast Eng 55(7–8):671–684
Ranasinghe R, Pattiaratchi C (1997) Investigation for Chilaw Anchorage: data report CTD measurements. January 1996. May 1996. WP 1296 RR, Centre for Water Research, The University of Western Australia, Australia
Ranasinghe R, Pattiaratchi C (1999) The seasonal closure of tidal inlets: Wilson Inlet – a case study. Coast Eng 37(1):37–56
Ranasinghe R, Pattiaratchi C, Masselink G (1999) A morphodynamic model to simulate the seasonal closure of tidal inlets. Coast Eng 37:1–36
Rosati JD, Gravens MB, Smith WG (1999) Regional sediment budget for Fire island to Montauk point, New York, USA. In: Proceedings of coastal sediments ’99, ASCE, New York, pp 803–817
Schwartz ML (ed) (1972) Spits and bars. Dowden, Hutchinson & Ross, Stroudsburg
Seabergh WC (1999) Physical model for coastal inlet entrance studies. CHETN-IV-19. Coastal and Hydraulics Laboratory, US Army Engineer Research and Development Center, Vicksburg
Shephard F (1952) Revised nomenclature for depositional coastal features. Am Assoc Pet Geol Bull 36:1902–1912
Smith WG, Watson K, Rahoy D, Rasmussen C, Headland JR (1999) Historic geomorphology and dynamics of Fire Island, Moriches and Shinnecock Inlets, New York. In: Proceedings of coastal sediments ’99, ASCE, New York, pp 1597–1612
Tanaka H, Takahashi F, Takahashi A (1996) Complete closure of the Nanakita River mouth in 1994. In: Proceedings of 25th coastal engineering conference, ASCE, Orlando, 4545–4556
Walton TL, Adams WD (1976) Capacity of inlet outer bars to store sand. In: Proceedings of 15th coastal engineering conference, ASCE, Honolulu, 1919–1937
Watanabe A, Shimizu T, Kondo K (1991) Field application of a numerical model of beach topography response. In: Proceedings of coastal sediments ’91, ASCE, Seattle, pp 1814–1828
Wheeler WH (1902) The sea-coast. Longmans, Green, and Co, London
Wikramanayake N, Pattiaratchi C (1999) Seasonal changes in a tidal inlet located in a monsoon regime. In: Proceedings of coastal sediments ’99, ASCE, New York, pp 1462–1477
Acknowledgements
This work was partially funded by the Regional Sediment Management Program under the Inlet Geomorphologic Work Unit of the Coastal Inlets Research Program of the U.S. Army Engineer Research and Development Center, and partly by Sida/SAREC under grants SWE-2005-332 and SWE-2010-038. Support was also provided by Sida/SAREC under grant 2011-002102 for continued bilateral research cooperation between Swedish institutions and Eduardo Mondlane University in Mozambique, Program Integrated Water Resources Management – Quantitative and Qualitative Aspects of IWRM for Sustainable Development in Southern Mozambique.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Larson, M., Palalane, J., Hanson, H. (2015). Sandy Spits and Their Mathematical Modeling. In: Randazzo, G., Jackson, D., Cooper, J. (eds) Sand and Gravel Spits. Coastal Research Library, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-13716-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-13716-2_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13715-5
Online ISBN: 978-3-319-13716-2
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)