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Horizontal wave propagation in the equatorial waveguide

Published online by Cambridge University Press:  26 April 2006

P. Ripa
P. Ripa
Affiliation:
Centro de Investigación Científica y de Educación Superior de Ensenada, Km. 107 Carr. Tijuana-Ensenada, (22860) Ensenada B. C., México
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Abstract

The dispersive (i.e. non-Kelvin) linear wave field on the equatorial β-plane, in a single vertical mode, is fully described by a single potential φ. Long Rossby waves, which are weakly dispersive, are represented in this field. This description is free from the problem of the ‘spurious solution’ encountered when working with an evolution equation for the meridional velocity; addition of this unwanted solution represents a gauge transformation that leaves the physical fields unaltered.

The general solution of the ray equations is found, including trajectories, and the amplitudes and phase fields. This solution is asymptotically valid for either high or low frequencies. The ray paths are identical in both limits, but the phase field is not, reflecting the isotropy of Poincaré waves, in one case, and the zonal anisotropy of Rossby waves, in the other.

Two examples are studied by ray theory: meridional normal modes and wave radiation from a point source in the equator. In the first case, the exact dispersion relation is obtained. In the second one, northern and southern caustics bend towards the equator, meeting there at focal points. The full solution is the superposition of many leaves and has a structure that would be hard to find in a normal modes expansion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 267 - 284
Copyright
© 1994 Cambridge University Press

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References

Blandford, R. 1966 Mixed gravity-Rossby waves in the oceans. Deep-Sea Res. 13, 941–961.Google Scholar
Cane, M. A. & Sarachik, E. S. 1979 Forced baroclinic ocean motion, III: The linear equatorial basin case. J. Mar. Res. 37, 355–398.Google Scholar
Chang, P. & Philander, S. G. H. 1988 Rossby wave packets in baroclinic mean currents. Deep-Sea Res. 36, 17–37.Google Scholar
Jacobs, S. J. 1967 An asymptotic solution of the tidal equations. J. Fluid Mech. 30, 417–438.Google Scholar
Kessler, W. S. 1990 Observations of long Rossby waves in the Northern Tropical Pacific. J. Geophys. Res. 95, 5183–5217.Google Scholar
Klauder, J. R. 1988 New asymptotics for old wave equations. Science 239, 760–762.Google Scholar
Laplace, P. S. de 1778 Recherches sur plusieurs points du système du monde. Mém. Acad. R. Sci. Paris 75–182.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Ludwig, D. 1966 Uniform asymptotic expansions at a caustic. Commun. Pure Appl. Maths 19, 215–250.Google Scholar
Matsuno, T. 1966 Quasi-geostrophic motions in the equatorial area. J. Met. Soc. Japan 48, 25–43.Google Scholar
McCreary, J. P. 1984 Equatorial beams. J. Mar. Res. 42, 395–430.Google Scholar
Moore, D. 1994 Equatorial waves and the effect of the horizontal component of the Earth's rotation. Geophys. Res. Lett. Submitted.Google Scholar
Moore, D. W. & Philander, S. G. H. 1977 Modelling of the tropical oceanic circulation. In The Sea, vol. 6 (ed. E. D. Goldberg, I. N. McCave, J. J. O'Brien & J. H. Steele), pp. 319–361. John Wiley.
Peregrine, D. H. & Smith, R. 1979 Nonlinear effects upon waves near caustics. Phil. Trans. R. Soc. Lond. A 268, 341–370.Google Scholar
Philander, S. G. H. 1977 The effect of coastal geometry on equatorial waves (Forced waves in the Gulf of Guinea). J. Mar. Res. 35, 509–523.Google Scholar
Ripa, P. 1982 Nonlinear wave–wave interactions in a one-layer reduced gravity model on the equatorial beta-plane. J. Phys. Oceanogr. 12, 97–111.Google Scholar
Ripa, P. 1983 Definite Integral of the product of Hermite functions, with applications to the theory of nonlinear interactions among equatorial waves. J. Geophys. Res. 88, 9741–9744.Google Scholar
Ripa, P. & Carrasco, A. C. 1993 Ray theory and the scattering of Topographic Rossby Waves by an abrupt change of shelf width and coastline. J. Geophys. Res. 98 C, 22693–22705.Google Scholar
Schopf, P., Anderson, D. L. T. & Smith, R. 1981 Beta-dispersion of low-frequency Rossby waves. Dyn. Atmos. Oceans 5, 187–214.Google Scholar
Wunsch, C. 1977 Response of an equatorial ocean to a periodic monsoon. J. Phys. Oceanogr. 7, 497–511.Google Scholar