Ocean Dynamics

, Volume 55, Issue 5–6, pp 549–558 | Cite as

Two-dimensional equilibrium morphological modelling of a tidal inlet: an entropy based approach

  • Joanna Marie Nield
  • David John Walker
  • Martin Francis Lambert
Original paper

Abstract

The management of tidal inlets requires the accurate prediction of equilibrium morphologies. In areas where the flow from rivers is highly regulated, it is important to give decision makers the ability to determine optimal flow management schemes, in order to allow tidal inlets to function as naturally as possible, and minimise the risk of inlet closure. The River Murray Mouth in South Australia is one such problem area. Drought and the retention of water for irrigation and urban water consumption have limited the amount of water entering the estuary. As a result, sediment from the coastal environment is being deposited in the mouth of the estuary, reducing the effect of further coastal interactions. Currently, situations such as this are modelled using traditional process-based methods, where wave, current, sediment transport and sediment balance modules are linked together in a time-stepping process. The modules are reapplied and assessed until a stable morphology is formed. In this paper, new options for modelling equilibrium morphologies of tidal inlets are detailed, which alleviate some of the shortfalls of traditional process-based models, such as the amplification of small errors and reliance on initial conditions. The modelling problem is approached in this paper from a different angle and involves the use of entropy based objective functions, which are optimised in order to find equilibrium morphologies. In this way, characteristics of a system at equilibrium can be recognised and a stable system predicted without having to step through time. This paper also details the use of self-organisation based modelling methods, another non-traditional model application, where local laws and feedback result in the formation of a global stable equilibrium morphology. These methods represent a different approach to traditional models, without some of the characteristics that may add to their limitations.

Keywords

Tidal inlet Morphological modelling Optimisation Entropy Self-organisation 

References

  1. Anderson RS, Bunas KL (1993) Grain size segregation and stratigraphy in aeolian ripples modelled with a cellular automaton. Nature 365(6448):740–743CrossRefGoogle Scholar
  2. Ashton A, Murray AB, Arnault O (2001) Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature 414:296–300CrossRefPubMedGoogle Scholar
  3. Blom A (2003) A vertical sorting model for rivers with non-uniform sediment and dunes. Universal Press, Veenendaal, The NetherlandsGoogle Scholar
  4. Caballeria M, Coco G, Falqués A, Huntley DA (2002) Self-organization mechanisms for the formation of nearshore crescentic and transverse sand bars. J Fluid Mech 465:379–410CrossRefGoogle Scholar
  5. Černý V (1985) Thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. J Optim Theor Appl 45(1):41–51CrossRefGoogle Scholar
  6. Coco G, Burnet TK, Werner BT, Elgar S (2004) The role of tides in beach cusp development. J Geophys Res 109(C4) (Art. No. C04011)Google Scholar
  7. Coulthard TJ, Macklin MG (2003) Modeling long-term contamination in river systems from historical metal mining. Geology 31(5):451–454CrossRefGoogle Scholar
  8. Cunha MC, Sousa J (2001) Hydraulic infrastructures design using simulated annealing. J Infrastruct Syst 7(1):32–39CrossRefGoogle Scholar
  9. de Boer DH (2001) Self-organization in fluvial landscapes: sediment dynamics as an emergent property. Comput Geosci 27:995–1003CrossRefGoogle Scholar
  10. Deng Z-Q, Singh VP (2002) Optimum channel pattern for environmentally sound training and management of alluvial rivers. Ecol Model 154:61–74CrossRefGoogle Scholar
  11. de Vriend HJ, Zyserman J, Nicholson J, Roelvink JA, Pechon P, Southgate HN (1993) Medium-term 2DH area modelling. Coast Eng 21:193–224CrossRefGoogle Scholar
  12. Friedrichs CT, Aubrey DG (1996) Uniform bottom shear stress and equilibrium hypsometry of intertidal flats. In: Pattiaratchi C (ed) Mixing in estuaries and coastal seas, coastal and estuarine studies. American Geophysical Union, Washington, pp 405–429Google Scholar
  13. Goldberg DE (1989) Genetic algorithms in search, optimisation and machine learning. Addison-Wesley, Reading, MAGoogle Scholar
  14. Hanson H, Aarninkhof S, Capobianco M, Jiménez JA, Larson M, Nicholls RJ, Plant NG, Southgate HN, Steetzel HJ, Stive MJF, de Vriend HJ (2003) Modelling of coastal evolution on yearly to decadal time scales. J Coast Res 19(4):790–811Google Scholar
  15. Hergarten S, Neugebauer HJ (2001) Self-organized critical drainage networks. Phys Rev Lett 86(12):2689–2692CrossRefPubMedGoogle Scholar
  16. Huang HQ, Chang HH, Nanson GC (2004) Minimum energy as the general form of critical flow and maximum flow efficiency and for explaining variations in river channel pattern. Water Resour Res 40(4) (Art. No. W04502)Google Scholar
  17. Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680CrossRefGoogle Scholar
  18. Leopold LB, Langbein WB (1962) The concept of entropy in landscape evolution. US Geol Surv Prof Pap 500-A:A1–A20Google Scholar
  19. Maritan A, Colaiori F, Flammini A, Cieplak M, Banavar JR (1996) Universality classes of optimal channel networks. Science 272(5264):984–986PubMedCrossRefGoogle Scholar
  20. Miao T-D, Mu Q-S, Wu S-Z (2001) Computer simulation of aeolian sand ripples and dunes. Phys Lett A 288:16–22CrossRefGoogle Scholar
  21. Molnár P, Ramírez JA (1998) Energy dissipation theories and optimal channel characteristics of river networks. Water Resour Res 34(7):1809–1818CrossRefGoogle Scholar
  22. Molnár P, Ramírez JA (2002) On downstream hydraulic geometry and optimal energy expenditure: case study of the Ashley and Taieri rivers. J Hydrol 259:105–115CrossRefGoogle Scholar
  23. Murray AB, Thieler ER (2004) A new hypothesis and exploratory model for the formation of large-scale inner-shelf sediment sorting and “rippled scour depressions”. Continent Shelf Res 24:295–315CrossRefGoogle Scholar
  24. Murray AB, Paola C (1994) A cellular model of braided rivers. Nature 371(6492):54–57CrossRefGoogle Scholar
  25. Rinaldo A, Rodríguez-Iturbe I, Rigon R (1998) Channel networks. Ann Rev Earth Planet Sci 26:289–327CrossRefGoogle Scholar
  26. Rodríguez-Iturbe, Rinaldo A, Rigon R, Bras RL, Marani A, Ijjász-Vásquez E (1992) Energy dissipation, runoff production, and the three-dimensional structure of river basins. Water Resour Res 28(4):1095–1103CrossRefGoogle Scholar
  27. van Rijn LC (1984) Sediment transport Part III: Bed forms and alluvial roughness. J Hydraul Div. Proc Am Soc Civ Eng 110(HY12):1733–1754CrossRefGoogle Scholar
  28. Wolfram S (2002) A new kind of science. Wolfram Media, Champaign, ILGoogle Scholar
  29. Walker DJ (1998) Modelling residence time in stormwater ponds. Ecol Eng 10(3):247–262CrossRefGoogle Scholar
  30. Wright DL, Coleman JM, Thom BG (1973) Processes of channel development in a high-tide-range environment: Cambridge Gulf-Ord River Delta, Western Australia. J Geol 81:15–41CrossRefGoogle Scholar
  31. Yang CT, Song CCS, Woldenberg MJ (1981) Hydraulic geometry and minimum rate of energy dissipation. Water Resour Res 17(4):1014–1018Google Scholar
  32. Yang CT (1971) Potential energy and stream morphology. Water Resour Res 7(2):311–322Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Joanna Marie Nield
    • 1
  • David John Walker
    • 1
  • Martin Francis Lambert
    • 1
  1. 1.School of Civil and Environmental EngineeringThe University of AdelaideAdelaideAustralia

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