A Semi-Implicit Semispectral Primitive Equation Model for Lake Circulation Dynamics and Its Stability Performance

Journal of Computational Physics

Volumn 139, Issue 1, 1998, Pages 209-241

  Wang, Yongqi ^a   Hutter, Kolumban ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Convergence; Lake circulation; Limnology; Oscillation; Semi implicit; Semispectral; Stability

Indexed keywords

EQUATIONS OF MOTION; INTEGRATION;

CONVERGENCE; INLAND LAKES; LAKE CIRCULATION; OSCILLATION; PRIMITIVE EQUATIONS MODELS; SEMI-IMPLICIT; SEMISPECTRAL; STABILITY PERFORMANCE; THREE-DIMENSIONAL NUMERICAL MODELS; TIME STEP;

LAKES;

EID: 0000282032     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5850     Document Type: Article

References (71)

1. J. Adams, MUDPACK: Multigrid software for linear elliptic partial differential equations, Version 3.0, National Center for Atmospheric Research, Boulder, CO, 1991. [Scientific Computing Division User Doc]
2. A. Arakawa and V. R. Larm, Computational design of the basic dynamical processes of the UCLA general circulation model, Methods Comput. Phys. 17, 173 (1977).
3. J. O. Backhaus and D. Hainbucher, A finite difference general circulation model for shelf seas and its application to low frequency variability on the North European Shelf, in Three-Dimensional Models of Marine and Estuarine Dynamics, edited by Nihoul and Jamart. Oceanography Series, Vol. 45 (Elsevier, Amsterdam, 1987), p. 221.
4. B. Barnier, P. Marchesiello, A. P. de Miranda, J.-M. Molines, and M. Coulibaly, A sigma-coordinate primitive equation model for studying the circulation in the South Atlantic. Part I. Model configuration with error estimates, Deep-Sea Res., in press (1997).
5. J. M. Beckers, Application of a 3D model to the Western Mediterranean, J. Marine Systems 1, 315 (1991).
6. A. Beckmann and D. B. Haidvogel, Numerical simulation of flow around a tall, isolated seamount. Part I. Problem formulation and model accuracy, J. Phys. Oceanogr. 23, 1736 (1993).
7. A. Beckmann and S. Diebels, Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane. Geophys. Astrophys. Fluid Dyn. 76, 95 (1994).
8. A. Beckmann and D. B. Haidvogel, A Numerical simulation of flow at Fieberling Guyot. J. Geophys. Res. 102, 5595 (1997).
9. J. R. Bennett, A three-dimensional model of Lake Ontario's summer circulation, Part I: Comparison with Observations. J. Phys. Oceanogr. 7, 591 (1977).
10. R. Bleck, C. Rooth, D. Hu, and L. Smith, Salinity-driven thermocline transients in a wind- and thermohaline-forced isopycnic coordinate model of the North Atlantic, J. Phys. Oceanogr. 22, 1486 (1992).
11. A. F. Blumberg and G. L. Mellor, A Description of a three-dimensional coastal ocean circulation model, in Three-dimensional Coastal Ocean Models, edited by Mooers. Coastal and Estuarine Sciences 4, 1 (1987).
12. D. C. Chapman and D. B. Haidvogel, Formation of Taylor caps over a tall isolated seamount in a stratified ocean. Geophys. Astrophys. Fluid Dyn. 64, 31 (1992).
13. D. C. Chapman and D. B. Haidvogel, Generation of internal lee waves over a tall isolated seamount. Geophys. Astrophys. Fluid Dyn. 69, 31 (1993).
14. M. D. Cox, A Primitive Equation Three-Dimensional Model of the Ocean, Tech. Rep. 1, GFDL Ocean Group, Princeton University, 1984.
15. G. T. Csanady, Water circulation and dispersal mechanisms, in Lakes: Chemistry, Geology, Physics, edited by A. Lerman (Springer-Verlag, New York/Heidelberg/Berlin, 1978).
16. G. T. Csanady, Circulation in the Coastal Ocean (Reidel, Dordrecht, 1984).
17. A. M. Davies, A three-dimensional numerical model of semi-diurnal tides on the European continental shelf, in Three-Dimensional Models of Marine and Estuarine Dynamics, edited by Nihoul and Jamart, Oceanography Series, Vol. 45 (Elsevier, Amsterdam, 1987), p. 573.
18. D. E. Dietrich, M. G. Marietta, and P. J. Roache, An ocean modelling system with turbulent boundary layers and topography: Model description, Int. J. Numer. Methods Fluids 7, 833 (1987).
19. J. W. Dippner, A frontal-resolving model for the German Bight, Continental Shelf Res. 13(1), 49 (1993).
20. W. Eifler and W. Schrimpf, ISPRAMIX, a hydrodynamic program for computing regional sea circulation patterns and transfer processes, Commission of the European Communities, EUR Report EUR 14856EN, 1992.
21. G. Z. Forristall, Three-dimensional structure of storm generated currents, J. Geophys. Res. 79, 2721 (1974).
22. I. Fukumori, J. Benveniste, C. Wunsch, and D. B. Haidvogel, Assimilation of sea surface topography into an ocean circulation model using a steady-state smoother, J. Phys. Oceanogr. 23, 1831 (1993).
23. D. B. Haidvogel, J. L. Wilkin, and R. Young, A semi-spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates, J. Comput. Phys. 94, 151 (1991).
24. D. B. Haidvogel, A. Beckmann, and K. S. Hedström, Dynamical simulations of filament formation and evolution in the coastal transition zone, J. Geophys. Res. 96, 15017 (1991).
25. D. B. Haidvogel, A. Beckmann, D. C. Chapman, and R.-Q. Lin, Numerical simulation of flow around a tall, isolated seamount. Part II. Resonant generation of trapped waves, J. Phys. Oceanogr. 23, 2373 (1993).
26. D. B. Haidvogel and A. Beckmann, Numerical models of the coastal ocean, The Sea, in press (1997).
27. P. F. Hamblin and E. Hollan, On the gravitational seiches of Lake Constance and their generation, Schweiz. Z. Hydrol. 40(1) (1978).
28. N. S. Heaps, Vertical structure of current in homogeneous and stratified waters, Hydrodynamics of Lakes, edited by K. Hutter (Springer-Verlag, Vienna/New York, 1984). [CISM-Lectures]
29. K. S. Hedström, User's Manual for a Semi-Spectral Primitive Equation Ocean Circulation Model (Institute for Naval Oceanography, Stennis Space Center, MS, 1990).
30. A. J. Hermann and H.-M. Hsu, A vertical coordinate mapping technique for semi-spectral primitive equation models of ocean circulation, J. Atmos. Ocean. Tech. 10, 381 (1993).
31. A. J. Hermann and W B. Owens, Energetics of gravitational adjustment for mesoscale chimneys, J. Phys. Oceanogr. 23, 346 (1993).
32. E. E. Hofmann, K. S. Hedström, J. R. Moisan, D. B. Haidvogel, and D. L. Mackas, Use of simulated drifter tracks to investigate general transport patterns and residence times in the coastal transition zone, J. Geophys. Res. 96, 15041 (1991).
33. E. Hollan, Strömungsmessungen im Bodensee, Sechster Ber. AWBR 6, 112 (1974).
34. E. Hollan and T. J. Simons, Wind-induced changes of temperature and currents in Lake Constance, Arch. Met. Geophys, Bioklim., Ser. A 27, 333 (1978).
35. K. Hutter and J. Trösch, Über diehydromechanischen und thermodynamischen Grundlagen der Seezirkulation, Mitteilung der Versuchasanstalt für Wasserbau, Hydrologie und Glaziologie, No. 20 (ETH, Zürich, 1975).
36. K. Hutter, G. Oman, and H. G. Ramming, Wind-bedingte Strömungen des homogenen Zürichsees. Mitteilung der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, No. 61 (ETH, Zürich, 1982).
37. K. Hutter, Fundamental equations and approximations, Hydrodynamics of Lakes, edited by K. Hutter (Springer-Verlag, Vienna/New York, 1984). [CISM-Lectures]
38. K. Hutter, Mathematische Vorhersage von barotropen und baroklinen Prozessen im Zürich und Luganersee. Vierteljahrschrifi der Naturforschenden Gesellschaft in Zürich. 129, 51 (1984).
39. K. Hutter, Hydrodynamic Modelling of Lakes. Transport Phenomena in the Environment, Gulf Publishing Company, Houston, 897 (1986).
40. K. Hutter, Großskalige Wasserbewegung in Seen: Grundlage der physikalischen Limnologie. Dynamik umweltrelevanter Systeme, edited by K. Hutter (Springer-Verlag, Berlin/Heidelberg/New York, 1991).
41. K. Hutter, Waves and Oscillations in the Ocean and in Lakes. Continuum Mechanics in Environmental Sciences and Geophysics, edited by K. Hutter (Springer-Verlag, Berlin/Heidelberg/New York, 1993).
42. K. Hutter, G. Bauer, Y Wang, and P. Güting, Forced response in enclosed lakes, IUTAM Symposium on Physical Limnology, Broome, Australia, September 3-8, 1995.
43. Internationale Gewässerschutzkomission für den Bodensee, Internationale Bodensee-Tiefenvermessung. Landesvermessungsamt Baden Württemberg (1990).
44. J. T. C. Ip and D. R. Lynch, Three-Dimensional Shallow Water Hydrodynamics on Finite Elements: Nonlinear Time-Stepping Prognostic Model, Report NML-94-1, Numerical Methods Laboratory, Dartmouth College, Hanover, NH, USA 03755, 1994.
45. M. Iskandarani, D. B. Haidvogel, and J. R Boyd, A staggered spectral element model with applications to the oceanic shallow water equations. International Journal of Numerical Methods in Fluids 20, 393 (1995).
46. A. Lehmann, Ein dreidimensionales baroklines wirbelauflösendes Modell der Ostsee. Ber. Inst. f. Meeresk., Kiel, No. 231, p. 104 (1992).
47. A. Lehmann, A three-dimensional baroclinic eddy resolving model of the Baltic Sea. Tellus A 47, 1013 (1995).
48. 6 and heat. Aquatic Sciences 56(4) (1994).
49. W H. Munk, On the wind-driven ocean circulation. J. Meteorology 7, 79 (1950).
50. G. Oman, Das Verhalten des geschichteten Zürichsees unter äusseren Windlasten. Mitteilung der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, No. 60 (ETH Zürich, 1982).
51. F. Peeters, Horizontale Mischung in Seen, Dissertation (ETH, Zürich, 1994).
52. T. Pohlmann, A three dimensional circulation model of the South China Sea, in Three-Dimensional Models of Marine and Estuarine Dynamics, edited by Nihoul and Jamart (1987), p. 245.
53. H.-G. Ramming and Z. Kowalik, Numerical Modelling of Marine Hydrodynamics, Oceanography Series, Vol. 26 (Elsevier, Amsterdam, 1980), p. 1.
54. R-T. Shaw, A numerical simulation of the evolution and propagation of gulf stream warm-core rings. J. Phys. Oceanogr. 24, 573 (1994).
55. T. J. Simons, Circulation Models of Lakes and Inland Seas, Canadian Bulletin of Fisheries and Aquatic Sciences. Bulletin 203, Ottawa, 1980.
56. S. Serruya, E. Hollan, and B. Bitsch, Steady winter circulations in Lakes Constance and Kinneret driven by wind and main tributaries, Arch. Hydrobiol. Suppl. 70(1), 32 (1984).
57. L. D. Spraggs and R. L. Street, Three-Dimensional Simulation of Thermally-Influenced Hydrodynamic Flows. Stanford University, Dept. of Civil Engineering, Technical Report 190, 1975.
58. Y Song and D. B. Haidvogel, A semi-implicit ocean circulation model using a generalized topography-following coordinate. J. Comput. Phys. 115, 228 (1994).
59. J. Sündermann, Die hydrodynamisch-numerische Berechnung der Vertikalstruktur von Bewegungsvorgängen in Kanälen und Becken, Mitt. Inst. Meereskunde Univ. Hamburg 19 (1971).
60. K.-T. Tee, Simple models to simulate three-dimensional tidal and residual cuurents, in Three-dimensional Coastal Ocean Models, edited by Mooers, Coastal and Estuarine Sciences 4, 125 (1987).
61. J. Trösch, Strömung in Seen - Dreidimensionale Simulation mit finiten Elementen. Mitteilung der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, No. 63 (ETH Zürich, 1983).
62. S. J. Walker, A 3-Dimensional Non-Linear Variable Density Hydrodynamic Model with Curvilinear Coordinates, Tech. Rep. OMR-60/00, CSIRO Division of Oceanography (in preparation, 1995).
63. J. Wang, L. A. Mysak, and R. G. Ingram, A three-dimensional numerical simulation of Hudson Bay summer ocean circulation: topographic gyres, separations and coastal jets. J. Phys. Oceangr. 24, 2496 (1994).
64. Y. Wang, Windgetriebene Strömungen in einem Rechteckbecken und im Bodensee, Shaker Verlag, Aachen (1996). Dissertation, Department of Mechanics, Technische Hochschule Darmstadt.
65. Y. Wang and K. Hutter, Three-dimensional wind-induced circulation in homogeneous lakes (in preparation, 1996).
66. Y Wang and K. Hutter, Three-dimensional wind-induced baroclinic circulation in a rectangle. A numerical treatment by a spectral model (in preparation, 1996).
67. Y Wang, K. Hutter, and E. Bäuerle, Three-dimensional wind-induced baroclinic circulation in Lake Constance (in preparation, 1996).
68. Y Wang and K. Hutter, ADI methods applied to a semi-spectral code of the shallow water equations (in preparation, 1997).
69. J. L. Wilkin and D. C. Chapman, Scattering of coastal-trapped waves by irregularities in coast-line and topography. J. Phys. Oceanogr. 20, 396 (1990).
70. J. L. Wilkin and K. S. Hedström, User's Manual for Orthogonal Curvilinear Grid-Generation Package. CSIRO (Hobart, Tasmania, Australia, 1991).
71. J. L. Wilkin, J. Mansbridge, and K. S. Hedström, An application of the capacitance matrix method to accomodate masked land areas and island circulations in a primitive equation ocean model. Int. J. Num. Meth. Fl. 20, 649 (1991).