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Journal of Physical Oceanography

  • Abramowitz, M., and A. Stegun, 1965: Handbook of Mathematical Functions. Dover, 1046 pp.

  • Chelton, D. B., and M. G. Schlax, 1996: Global observations of oceanic Rossby waves. Science, 272 , 234–238.

  • Flierl, G. R., 1977: Simple applications of McWilliams' “A note on a consistent quasigeostrophic model in a multiply connected domain.”. Dyn. Atmos. Oceans, 1 , 443–453.

    • Search Google Scholar
    • Export Citation

  • Gerdes, R., and C. Wübber, 1991: Seasonal variability of the North Atlantic Ocean—A model intercomparison. J. Phys. Oceanogr, 21 , 1300–1322.

    • Search Google Scholar
    • Export Citation

  • Gordon, C., D. L. Webb, and S. Wolpert, 1992: One cannot hear the shape of a drum. Bull. Amer. Math. Soc, 27 , 134–138.

  • Harlander, U., A. Gassmann, and W. Metz, 2001: Stationary Rossby wave propagation in a shear flow along a reflecting boundary. Meteor. Atmos. Phys, 78 , 245–260.

    • Search Google Scholar
    • Export Citation

  • Harlander, U., H-J. Schönfeldt, and W. Metz, 2000: Rossby waveguides in high-latitude shear flows with boundaries. J. Geophys. Res, 105 , 17063–17078.

    • Search Google Scholar
    • Export Citation

  • Holland, W. R., 1978: The role of mesoscale eddies in the general circulation of the ocean—Numerical experiments using a wind driven quasi-geostrophic model. J. Phys. Oceanogr, 8 , 363–392.

    • Search Google Scholar
    • Export Citation

  • Jensen, F. B., W. A. Kuperman, M. B. Porter, and H. Schmidt, 2000: Computational Ocean Acoustics. Springer-Verlag, 480 pp.

  • Kac, M., 1966: Can one hear the shape of a drum? Amer. Math. Mon, 73B , 1–23.

  • LaCasce, J. H., and J. Pedlosky, 2002: Baroclinic Rossby waves in irregular basins. J. Phys. Oceanogr, 32 , 2828–2847.

  • LeBlond, P. H., and L. A. Mysak, 1978: Waves in the Ocean. Oceanography Series, Elsevier, 602 pp.

  • Maas, L. R. M., D. Benielli, J. Sommeria, and F-P. A. Lam, 1997: Observation of an internal wave attractor in a confined, stable stratified fluid. Nature, 388 , 557–561.

    • Search Google Scholar
    • Export Citation

  • McCartin, B. J., 2003: Eigenstructure of the equilateral triangle, Part I: The Dirichlet problem. SIAM Rev, 45 , 267–287.

  • McWilliams, J. C., 1977: A note on a consistent quasigeostrophic model in a multiply connected domain. Dyn. Atmos. Ocean, 1 , 427–441.

  • Nedelec, J-C., 2001: Acoustic and Electromagnetic Equations. Springer-Verlag, 316 pp.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed. Springer-Verlag, 710 pp.

  • Platzman, G. W., 1978: Normal modes of the World Ocean, Part I: Design of a finite-element barotropic model. J. Phys. Oceanogr, 8 , 323–343.

    • Search Google Scholar
    • Export Citation

  • Polyanin, A. D., 2002: Handbook of Linear Partial Differential Equations for Engineers and Scientists. CRC Press, 500 pp.

  • Primeau, F., 2002: Long Rossby wave basin-crossing time and the resonance of low-frequency basin modes. J. Phys. Oceanogr, 32 , 2652–2665.

    • Search Google Scholar
    • Export Citation

  • Rhines, P., 1970: Edge-, bottom-, and Rossby waves in a rotating stratified fluid. Geophys. Fluid. Dyn, 1 , 273–302.

  • Sheremet, V. A., G. R. Ierley, and V. M. Kamenkovich, 1997: Eigenanalysis of the two-dimensional wind-driven ocean circulation problem. J. Mar. Res, 55 , 57–92.

    • Search Google Scholar
    • Export Citation

  • Stöckmann, H-J., 1999: Quantum Chaos. Cambridge University Press, 368 pp.

  • Straub, D. N., 1994: Dispersive effects of zonally varying topography on quasi-geostrophic Rossby waves. Geophys. Astrophys. Fluid Dyn, 75 , 107–130.

    • Search Google Scholar
    • Export Citation

  • Tailleux, R., and J. C. McWilliams, 2002: Energy propagation of long extratropical Rossby waves over slowly varying zonal topography. J. Fluid Mech, 473 , 295–319.

    • Search Google Scholar
    • Export Citation

  • Zaitsev, O., R. Narevich, and R. E. Prange, 2001: Quasiclassical Born-Oppenheimer approximations. Found. Phys, 31 (1) 7–26.

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Article Type:
Research Article

On Quasigeostrophic Normal Modes in Ocean Models: Weakly Nonseparable Situation

Uwe Harlander1 and Leo R. M. Maas1
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  • 1 Netherlands Institute for Sea Research, Texel, Netherlands
Print Publication:
01 Sep 2004
DOI:
https://doi.org/10.1175/1520-0485(2004)034<2086:OQNMIO>2.0.CO;2
Page(s):
2086–2095
Restricted access

Abstract

This study examines quasigeostrophic Rossby eigenmodes of homogeneous as well as stratified oceans. Analytical studies of Rossby basin modes are usually done by using simple basin geometries. Simple means that solutions are available by applying a separation ansatz in looking for basin modes. Here the focus is on half-trapezoidal geometry, in particular on a stratified ocean with a half-trapezoidal (zonal) cross section. In this case, separation is not possible. However, approximate solutions can be found. Different approximations are discussed: one related to linearization of the boundary conditions, one related to a sight change in boundary geometry, and one that uses an asymptotic expansion. It is shown that the widely used “linearized boundary conditions” give wrong results for low-frequency modes. The reason is that weak asymmetries of the basin are neglected and wave energy is therefore distributed too homogeneously in the basin. Although the basin's geometry used deviates only slightly from a square and the eigenvalue spectrum corresponds well with that of a square basin, eigenmodes can still differ greatly.

Corresponding author address: Uwe Harlander, The Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Texel, Netherlands. Email: harland@nioz.nl

Abstract

This study examines quasigeostrophic Rossby eigenmodes of homogeneous as well as stratified oceans. Analytical studies of Rossby basin modes are usually done by using simple basin geometries. Simple means that solutions are available by applying a separation ansatz in looking for basin modes. Here the focus is on half-trapezoidal geometry, in particular on a stratified ocean with a half-trapezoidal (zonal) cross section. In this case, separation is not possible. However, approximate solutions can be found. Different approximations are discussed: one related to linearization of the boundary conditions, one related to a sight change in boundary geometry, and one that uses an asymptotic expansion. It is shown that the widely used “linearized boundary conditions” give wrong results for low-frequency modes. The reason is that weak asymmetries of the basin are neglected and wave energy is therefore distributed too homogeneously in the basin. Although the basin's geometry used deviates only slightly from a square and the eigenvalue spectrum corresponds well with that of a square basin, eigenmodes can still differ greatly.

Corresponding author address: Uwe Harlander, The Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Texel, Netherlands. Email: harland@nioz.nl

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