Three-dimensional hydrodynamic model for wind-driven circulation

  • C. L. N. Cunha
  • A. C. Scudelari
  • P. C. C. Rosman
Technical Paper

Abstract

This paper presents the development of a three-dimensional hydrodynamic model for wind-driven circulation using the moving element method in the vertical discretization. As most three-dimensional models use sigma coordinate transformation in the vertical discretization, the use of the moving element method is an alternative to the latter, with the advantage that there is no need for fixed subdivision of the water column. In the proposed model, the coupling of two- and three-dimensional hydrodynamic model is considered. The shallow-water equations are integrated in the vertical direction, finite elements are employed in the spatial discretization, and finite differences in the time discretization, to resolve the position of the free surface (ζ), and the vertically integrated velocities components. The three-dimensional module is used to compute the velocity profiles. In the three-dimensional module is employed the moving element method in the vertical discretization. The efficiency of the model is demonstrated through the comparison of its results with laboratory experimental results and with another model that uses sigma coordinate transformation in the vertical discretization.

Keywords

Three-dimensional model Semi-implicit model Shallow-water equation Wind-driven circulation 

References

  1. 1.
    Baines MJ, Hubbard ME, Jimack PK (2005) A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries. Appl Numer Math 54:450–469MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bijvelds MJP, Kranenburg C, Stelling GS (1999) 3D numerical simulation of turbulent shallow-water flow in square harbor. J Hydraul Eng 125:26–31CrossRefGoogle Scholar
  3. 3.
    Brebbia CA, Ferrante AJ (1975) The finite element technique. Editora da URGS, Porto Alegre Google Scholar
  4. 4.
    Casulli V, Stelling GS (2011) Semi-implicit subgrid modelling of three-dimensional free-surface flows. Int J Numer Methods Fluids 67:441–449MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Casulli V (1997) Numerical simulation of three-dimensional free surface flow in isopycnal coordinates. Int J Numer Methods Fluids 25:645–658CrossRefMATHGoogle Scholar
  6. 6.
    Cea L, Stelling GS, Zijlema M (2009) Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation. Int J Numer Methods Fluids 61:382–410MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cunha CLN, Rosman PCC (2005) A semi-implicit finite element model for natural water bodies. Water Res 39:2034–2047CrossRefGoogle Scholar
  8. 8.
    Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Mixing in island and coastal water. Academic Press, New YorkGoogle Scholar
  9. 9.
    Ham DA, Pietrzak J, Stelling GS (2005) A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations. Ocean Model 10:153–169CrossRefGoogle Scholar
  10. 10.
    Hulscher SJMH (1996) Tidal-induced large-scale regular beds form patterns in a three-dimensional shallow water model. J Geophys Res 101:727–744CrossRefGoogle Scholar
  11. 11.
    Jin XY (1993) Quasi-three-dimensional numerical modeling of flow and dispersion in shallow water. Report 93-3 Ph.D. Thesis, Department of Civil Engineering, Delft University of TechnologyGoogle Scholar
  12. 12.
    Johns B (1991) The modeling of the free surface flow of water over topography. Coast Eng 15:257–278CrossRefGoogle Scholar
  13. 13.
    Koçyigit MB, Falconer RA (2004) Three-dimensional numerical modeling of wind-driven circulation in a homogeneous lake. Adv Water Resour 27:1167–1178CrossRefGoogle Scholar
  14. 14.
    Levasseur A, Shi L, Wells NC, Purdie DA, Kelly-Gerreyn BA (2007) A three-dimensional hydrodynamic model of estuarine circulation with an application to Southampton Water, UK. Estuar Coast Shelf Sci 73:753–767CrossRefGoogle Scholar
  15. 15.
    Li YS, Zhan JM (1993) An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows. Int J Numer Methods Fluids 16:187–198CrossRefMATHGoogle Scholar
  16. 16.
    Liu W, Chen W, Kuo J, Wu C (2008) Numerical determination of residence time and age in a partially mixed estuary using three-dimensional hydrodynamic model. Cont Shelf Res 28:1068–1088CrossRefGoogle Scholar
  17. 17.
    Mahadevan A, Oliger J, Street R (1996) A nonhydrostatic mesoscale ocean model. Part II: numerical implemention. J Phys Oceanogr 26:1881–1900CrossRefGoogle Scholar
  18. 18.
    Muccino JC, Gray WG, Oreman GG (1997) Calculation of vertical velocity in three-dimensional, shallow water equation, finite elements models. Int J Numer Methods Fluids 25:779–802CrossRefMATHGoogle Scholar
  19. 19.
    Muin M, Spaulding M (1997) Three-dimensional boundary-fitted circulation model. J Hydraul Eng 123:1–12Google Scholar
  20. 20.
    Ng EYK, Liu SZ (1997) A novel implicit difference algorithm of primite variable flow equation with higher order extra terms. Comput Fluids 26:163–182MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Rosman PCC (1987) Modeling shallow water bodies via filtering techniques. Ph.D. Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, USAGoogle Scholar
  22. 22.
    Rosman PCC, Gobbi EF (1990) A self-adjusting grid turbulence model for shallow water flow. XI Congresso Ibero Latino Americano sobre Métodos Computacionais para EngenhariaGoogle Scholar
  23. 23.
    Rosso TCA, Rosman PCC (1997) Hydrodynamic model for floating contaminants transport in coastal regions. Offshore Eng Trans Built Environ 29:113–124Google Scholar
  24. 24.
    Scudelari AC (1997) Development of a moving element method for the shallow water equations. D.Sc. Thesis, COPPE/UFRJ (in Portuguese). http://www.coc.ufrj.br/index.php?option=com_content&view=article&id=831:ada-cristina-scudelari&catid=141&Itemid=154&lang=pt-br. Accessed 04 Jul 2017
  25. 25.
    Sheng YP (1987) Modeling three-dimensional estuarine hydrodynamics. In: Nohoul JCJ, Jamart BM (eds) Three-dimensional modeling of marine and estuarine dynamics. Elsevier, AmsterdamGoogle Scholar
  26. 26.
    Stansby PK, Zhou JG (1997) Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems. Int J Numer Methods Fluids 28:541–563CrossRefMATHGoogle Scholar
  27. 27.
    Stockstill RL (1997) Implicit moving finite element model of the 2D shallow-water equations. Trans Model Simul 17:199–208Google Scholar
  28. 28.
    Vanzo D, Siviglia A, Toro EF (2016) Pollutant transport by shallow water equations on unstructured meshes. J Comput Phys 321:1–20MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Wai OWH, Lu Q, Li YS (1996) Multi-layer modeling of three-dimensional hydrodynamic transport processes. J Hydraul Res 34:677–693CrossRefGoogle Scholar
  30. 30.
    Wu J (1982) Wind-stress coefficients over sea surface from breeze to hurricane. J Geophys Res 87:9704–9706CrossRefGoogle Scholar
  31. 31.
    Yu X (1987) Turbulent channel flow under the action of surface wind-stress. Internal Report No. 2-87, Laboratory of Fluid Mechanics, Department of Civil Engineering, Delft University of Technology. http://repository.tudelft.nl/islandora/object/uuid:a969aa64-d8a6-4a08-a494-71eb4149eb5d/?collection=research. Accessed 03 Jul 2017
  32. 32.
    Zounemat-Kermani M, Sabbagh-Yazdi S (2010) Coupling of two- and three-dimensional hydrodynamic numerical models for simulating wind-induced currents in deep basins. Comput Fluids 39:994–1011MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • C. L. N. Cunha
    • 1
  • A. C. Scudelari
    • 2
  • P. C. C. Rosman
    • 3
  1. 1.Programa de Pós-Graduação em Engenharia AmbientalUniversidade Federal do ParanáCuritibaBrazil
  2. 2.Programa de Pós-graduação em Engenharia SanitáriaUniversidade Federal do Rio Grande do NorteNatalBrazil
  3. 3.Programa de Engenharia Oceânica, COPPEUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

Personalised recommendations