Triad instability of planetary rossby waves
MetadataShow full item record
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.
Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 2158–2171, doi:10.1175/jpo3100.1.
Showing items related by title, author, creator and subject.
Estimation of planetary wave parameters from the data of the 1981 ocean acoustic tomography experiment Chiu, Ching-Sang (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1985-08)Using the maximum-likelihood estimation method and minimization techniques, quasi-geostrophic wave solutions were fitted to the observations of the 1981 Ocean Acoustic Tomography Experiment. The experiment occupied a ...
Pedlosky, Joseph; Iacono, Roberto; Napolitano, Ernesto; Helfrich, Karl R. (Sears Foundation for Marine Research, 2009-09)The flow around planetary scale islands is examined when the island possesses a topographic skirt representing a steep continental shelf. The model is barotropic and governed by the shallow water equations and the motion ...
Beron-Vera, F. J.; Brown, Michael G.; Olascoaga, M. J.; Rypina, Irina I.; Kocak, H.; Udovydchenkov, Ilya A. (American Meteorological Society, 2008-10)The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV staircase model is used to illustrate ...