• Chelton, D. B., , and M. G. Schlax, 1996: Global observations of oceanic Rossby waves. Science, 272 , 234238.

  • Chelton, D. B., , R. A. deSzoeke, , M. G. Schlax, , K. El Naggar, , and N. Siwertz, 1998: Geographical variability of the first-baroclinic Rossby radius of deformation. J. Phys. Oceanogr., 28 , 433460.

    • Search Google Scholar
    • Export Citation
  • Isachsen, P. E., , J. H. LaCasce, , and J. Pedlosky, 2007: Rossby wave instability and apparent phase speeds in large ocean basins. J. Phys. Oceanogr., 37 , 11771191.

    • Search Google Scholar
    • Export Citation
  • LaCasce, J. H., , and J. Pedlosky, 2004: The instability of Rossby basin modes and the oceanic eddy field. J. Phys. Oceanogr., 34 , 20272041.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., , W. Miao, , and P. Muller, 1997: Propagation and decay of forced and free baroclinic Rossby waves in off-equatorial oceans. J. Phys. Oceanogr., 27 , 24052417.

    • Search Google Scholar
    • Export Citation
  • Schopf, P. S., , D. L. T. Anderson, , and R. Smith, 1981: Beta-dispersion of low-frequency Rossby waves. Dyn. Atmos. Oceans, 5 , 187214.

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Triad Instability of Planetary Rossby Waves

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  • 1 Massachusetts Institute of Technology–Woods Hole Oceanographic Institution Joint Program in Oceanography and Ocean Engineering, Cambridge, Massachusetts
  • | 2 Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

The triad instability of the large-scale, first-mode, baroclinic Rossby waves is studied in the context of the planetary scale when the Coriolis parameter is to its lowest order varying with latitude. Accordingly, rather than remain constant as in quasigeostrophic theory, the deformation radius also changes with latitude, yielding new and interesting features to the propagation and triad instability processes. On the planetary scale, baroclinic waves vary their meridional wavenumbers along group velocity rays while they conserve both frequencies and zonal wavenumbers. The amplitudes of both barotropic and baroclinic waves would change with latitude along a ray path in the same way that the Coriolis parameter does if effects of the nonlinear interaction are ignored. The triad interaction for a specific triad is localized within a small latitudinal band where the resonance conditions are satisfied and quasigeostrophic theory is applicable locally. Using the growth rate from that theory as a measure, at each latitude along the ray path of the basic wave, a barotropic wave and a secondary baroclinic wave are picked up to form the most unstable triad and the distribution of this maximum growth rate is examined. It is found to increase southward under the assumption that triad interactions do not cause a noticeable decrease in the quantity of the basic wave’s amplitude divided by the Coriolis parameter. Different barotropic waves that maximize the growth rate at different latitudes have almost the same meridional length scale, on the order of the deformation radius. With many rays starting from different latitudes on the eastern boundary and with wavenumbers on each of them satisfying the no-normal-flow condition, the resulting two-dimensional distribution of the growth rate is a complicated function of the relative relations of zonal wavenumbers or frequencies on different rays and the orientation of the eastern boundary. In general, the growth rate is largest on rays originating to the north.

Corresponding author address: Yu Zhang, 77 Massachusetts Avenue, Room 54-1421, Massachusetts Institute of Technology, Cambridge, MA 02139. Email: sophiezy@mit.edu

Abstract

The triad instability of the large-scale, first-mode, baroclinic Rossby waves is studied in the context of the planetary scale when the Coriolis parameter is to its lowest order varying with latitude. Accordingly, rather than remain constant as in quasigeostrophic theory, the deformation radius also changes with latitude, yielding new and interesting features to the propagation and triad instability processes. On the planetary scale, baroclinic waves vary their meridional wavenumbers along group velocity rays while they conserve both frequencies and zonal wavenumbers. The amplitudes of both barotropic and baroclinic waves would change with latitude along a ray path in the same way that the Coriolis parameter does if effects of the nonlinear interaction are ignored. The triad interaction for a specific triad is localized within a small latitudinal band where the resonance conditions are satisfied and quasigeostrophic theory is applicable locally. Using the growth rate from that theory as a measure, at each latitude along the ray path of the basic wave, a barotropic wave and a secondary baroclinic wave are picked up to form the most unstable triad and the distribution of this maximum growth rate is examined. It is found to increase southward under the assumption that triad interactions do not cause a noticeable decrease in the quantity of the basic wave’s amplitude divided by the Coriolis parameter. Different barotropic waves that maximize the growth rate at different latitudes have almost the same meridional length scale, on the order of the deformation radius. With many rays starting from different latitudes on the eastern boundary and with wavenumbers on each of them satisfying the no-normal-flow condition, the resulting two-dimensional distribution of the growth rate is a complicated function of the relative relations of zonal wavenumbers or frequencies on different rays and the orientation of the eastern boundary. In general, the growth rate is largest on rays originating to the north.

Corresponding author address: Yu Zhang, 77 Massachusetts Avenue, Room 54-1421, Massachusetts Institute of Technology, Cambridge, MA 02139. Email: sophiezy@mit.edu

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