Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T21:38:30.610Z Has data issue: false hasContentIssue false
  • English
  • Français

On coastal trapped waves at low latitudes in a stratified ocean

Published online by Cambridge University Press:  19 April 2006

J. S. Allen  and
R. D. Romea
J. S. Allen
Affiliation:
School of Oceanography, Oregon State University, Corvallis, Oregon 97331
R. D. Romea
Affiliation:
School of Oceanography, Oregon State University, Corvallis, Oregon 97331
Get access Rights & Permissions [Opens in a new window]

Abstract

Results from idealized ocean models indicate that equatorially trapped baroclinic waves incident on an eastern boundary may be partially transmitted north and south along the coast as boundary-trapped internal Kelvin waves. The offshore scale of the coastal internal Kelvin waves is the internal Rossby radius of deformation δR, which decreases as the Coriolis parameter f increases. The effect of the presence of a continental slope of width Ls, along a north–south oriented coastline, on the poleward propagation of coastal trapped internal Kelvin waves is studied in a two-layer β-plane model. The waves propagate from regions near the equator where δR > Ls to mid-latitudes where δR < Ls. It is assumed that f varies slowly on the alongshore scale of the waves L, that L [Gt ] Ls, and that either the topographic slope is weak or that the upper-layer depth is small compared to the lower-layer depth. All of the coastal trapped waves present in the model are non-dispersive. For most values of f, the cross-shelf eigen-functions consist of the internal Kelvin wave and an infinite set of continental shelf waves whose vertical structure depends on δR/Ls. For δR/Ls [Gt ] 1, the shelf waves are bottom trapped while for δR/Ls [Lt ] 1 they are barotropic. The wave speeds Cn of the shelf waves vary linearly with f, whereas the wave speed c0 of the internal Kelvin wave is independent of f. As f increases through critical values fCn, where Cn approaches C0, the phase speeds and the eigenfunctions vary so that the eigenfunctions represent a different type of wave on either side of fCn. In the slowly-varying approximation, the alongshore energy flux in each eigenfunction is a constant. It follows that an internal Kelvin wave which has a wavelength short enough that the slowly-varying approximation remains valid and which propagates poleward from the equatorial region where f < fC1 will transform into a shelf wave, at values of f near fC1, and will continue propagation poleward in that form. As a result, coastal trapped baroclinic disturbances may be able to propagate efficiently from the equatorial region to mid-latitudes where they may take the form of barotropic shelf waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 3 , 12 June 1980 , pp. 555 - 585
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. S. 1975 Coastal trapped waves in a stratified ocean. J. Phys. Oceanog. 5, 300–325.Google Scholar
Anderson, D. L. T. & Rowlands, P. B. 1976 The role of inertia-gravity and planetary waves in the response of a tropical ocean to the incidence of an equatorial Kelvin wave on a meridional boundary. J. Mar. Res. 34, 395–417.Google Scholar
Bretherton, F. P. 1968 Propagation in slowly varying waveguides. Proc. Roy. Soc. A 302, 555–576.Google Scholar
Brink, K. H., Allen, J. S. & Smith, R. L. 1978 A study of low-frequency fluctuations near the Peru coast. J. Phys. Oceanog. 8, 1025–1041.Google Scholar
Buchwald, V. T. & Adams, J. K. 1968 The propagation of continental shelf waves. Proc. Roy. Soc. A 305, 235–250.Google Scholar
Cane, M. A. & Sarachik, E. S. 1976 Forced baroclinic ocean motions: I. The linear equatorial unbounded case. J. Mar. Res. 34, 629–665.Google Scholar
Cane, M. A. & Sarachik, E. S. 1977 Forced baroclinic ocean motions. II. The linear equatorial bounded case. J. Mar. Res. 35, 395–432.Google Scholar
Garrett, C. J. R. 1969 Atmospheric edge waves. Quart. Jl R. Met. Soc. 95, 731–753.Google Scholar
Gill, A. E. & Schumann, E. H. 1974 The generation of long shelf waves by wind. J. Phys. Oceanog. 4, 83–90.Google Scholar
Grimshaw, R. 1977 The effects of a variable Coriolis parameter, coastline curvature and variable bottom topography on continental-shelf waves. J. Phys. Oceanog. 7, 547–554.Google Scholar
Grimshaw, R. & Allen, J. S. 1979 Linearly coupled, slowly varying oscillators. Stud. appl. Math. 66, 51–71.Google Scholar
Hurlburt, H. E., Kindle, J. C. & O'Brien, J. J. 1976 A numerical simulation of the onset of El Niño. J. Phys. Oceanog. 6, 621–631.Google Scholar
Huyer, A., Hickey, B. M., Smith, J. D. & Pillsbury, R. D. 1975 Alongshore coherence at low frequencies in currents observed over the continental shelf off Oregon and Washington. J. Geophys. Res. 80, 3495–3505.Google Scholar
Ince, E. L. 1956 Ordinary Differential Equations, p. 205. Dover.
Kundu, P. K. & Allen, J. S. 1976 Some three-dimensional characteristics of low-frequency current fluctuations near the Oregon Coast. J. Phys. Oceanogr. 6, 181–199.Google Scholar
Lighthill, J. J. 1969 Dynamic response of the Indian Ocean to the onset of the Southwest Monsoon. Phil. Trans. Roy. Soc. A 265, 45–92.Google Scholar
McCreary, J. 1976 Eastern tropical ocean response to changing wind systems with application to El Niño. J. Phys. Oceanog. 6, 632–645.Google Scholar
Miles, J. W. 1972 Kelvin waves on oceanic boundaries. J. Fluid Mech. 55, 113–127.Google Scholar
Moore, D. W. 1968 Planetary-gravity waves in an equatorial ocean. Ph.D. thesis, Harvard University.
Moore, D. W. & Philander, S. G. H. 1977 Modeling of the tropical ocean circulation. The Sea, vol. vi (ed. E. D. Goldberg et al.), cha. 8. Wiley-Interscience.
Rhines, P. 1970 Edge, bottom and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn. 1, 273–302.Google Scholar
Smith, R. L. 1978 Poleward propagating perturbations in sea level and currents along the Peru coast. J. Geophys. Res. 83, 6083–6092.Google Scholar
Wang, D. P. & Mooers, C. N. K. 1976 Coastal trapped waves in a continuously stratified ocean. J. Phys. Oceanog. 6, 853–863.Google Scholar
Wyrtki, K. 1964 The thermal structure of the Eastern Pacific Ocean. Dt. hydrogr. Z., Erganzungsh. A 6.Google Scholar