Beta-dispersion of low-frequency Rossby waves |
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| Authors: | Paul S Schopf David LT Anderson Ronald Smith |
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| Institution: | 1. Laboratory for Atmospheric Sciences (GLAS), NASA/Goddard Space Flight Center, Greenbelt, MD 20771 U.S.A.;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Great Britain |
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| Abstract: | An investigation is made into the dispersion of oceanic internal Rossby waves at annual and semi-annual frequencies. Turning of the group velocity vector due to latitudinal variations in the radius of deformation cannot be neglected, particularly in basins as large as the Pacific. This turning allows disturbances to propagate from high lattitudes into the equatorial zone and distorts the solutions in the western part of the basin. For no mean flow, and a coastline aligned north-south, an almost exact focus of wave energy is found very close to the equator at a distance of just under from the eastern boundary, where is the eigenspeed of a high-frequency internal wave mode, and ω is the angular frequency of the low-frequency wave being studied. The focus depends on a long meridional wavelength excited at the coast, and a frequency small compared with , where is the radius of the Earth. For the lowest baroclinic mode and waves of annual period, this distance is about 12 000 km. Equivalence of the ray theory and the theory of equatorial meridional modes is demonstrated for the simple cases where the latter applies.The effects of mean currents and irregular coastlines are examined. Barotropic mean currents may change the turning latitude and ray shapes, inducing critical layers and enhancing reflection. Baroclinic mean currents are seen to affect the rays by simply changing the speed in proportion to the depth of the thermocline. As long as the mean currents are geostrophically balanced, no “effective beta” term from variations in the thermocline depth appears, in contrast to the topographic Rossby wave problem. |
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