×

Barotropic-baroclinic time splitting for ocean circulation modeling. (English) Zbl 0888.76055

We develop a new splitting procedure by using nonlinear primitive equations. We analyze the stability of this splitting when applied to a linearized flow in a two-layer fluid with one horizontal dimension and a flat lower boundary. Then we extend this analysis to the case of two horizontal dimensions in a rotating reference frame with constant Coriolis parameter. Some numerical tests of the new splitting are described.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bleck, R.; Smith, L. T., A wind-driven isopycnic coordinate model of the north and equatorial Atlantic Ocean 1. Model development and supporting experiments, J. Geophys. Res. C, 95, 3273 (1990)
[2] Bleck, R.; Rooth, C.; Hu, D.; Smith, L. T., Salinity-driven thermocline transients in a wind- and thermohaline-forced isopycnic coordinate model of the North Atlantic, J. Phys. Oceanogr., 22, 1486 (1992)
[3] Bryan, K., A numerical method for the study of the circulation of the world ocean, J. Comput. Phys., 4, 347 (1969) · Zbl 0195.55504
[4] Davis, R. E., Diapycnal mixing in the ocean: equations for large-scale budgets, J. Phys. Oceanogr., 24, 777 (1994)
[5] Dukowicz, J. K.; Smith, R. D., Implicit free-surface method for the Bryan-Cox-Semtner ocean model, J. Geophys. Res. C, 99, 7991 (1994)
[6] Gill, A. E., Atmosphere-Ocean Dynamics (1982), Academic Press: Academic Press San Diego
[7] Haltiner, G. J.; Williams, R. T., Numerical Prediction and Dynamic Meteorology (1980), Wiley: Wiley New York
[8] Higdon, R. L.; Bennett, A. F., Stability analysis of operator splitting for large-scale ocean modeling, J. Comput. Phys., 123, 311 (1996) · Zbl 0863.76045
[9] Killworth, P. D.; Stainforth, D.; Webb, D. J.; Paterson, S. M., The development of a free-surface Bryan-Cox-Semtner ocean model, J. Phys. Oceanogr., 21, 1333 (1991)
[10] Mesinger, F.; Arakawa, A., Numerical Methods Used in Atmospheric Models. Numerical Methods Used in Atmospheric Models, GARP Publications Series No. 17, 1 (1976), WMO-ICSU Joint Organizing Committee: WMO-ICSU Joint Organizing Committee Geneva
[11] Oberhuber, J. M., Simulation of the Atlantic circulation with a coupled sea ice—mixed layer—isopycnal general circulation model. Part I. Model description, J. Phys. Oceanogr., 23, 808 (1993)
[12] Pedlosky, J., Geophysical Fluid Dynamics (1987), Springer-Verlag: Springer-Verlag New York · Zbl 0713.76005
[13] Semtner, A. J., Finite-difference formulation of a world ocean model, Advanced Physical Oceanographic Numerical Modelling (1986), Reidel: Reidel Norwell, p. 187-
[14] J. Wang, M. Ikeda, On inertial stability and phase error of time integration schemes in ocean general circulation models, Mon. Weather Rev.; J. Wang, M. Ikeda, On inertial stability and phase error of time integration schemes in ocean general circulation models, Mon. Weather Rev.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.