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Coastal Kelvin waves in the presence of a slowly varying topography

Published online by Cambridge University Press:  26 April 2006

Ping Chang
Ping Chang
Affiliation:
The Joint Institute of the Study of the Atmosphere and Oceans, University of Washington, AK-40, Seattle, WA 98195, USA Present address: Department of Oceanography, Texas A&M University. College Station, TX 77843, USA.
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Abstract

The evolution equation is derived for a weakly nonlinear coastal Kelvin wave propagating in slowly varying topography in an f-plane ocean. For weak transverse variations in the topography, the wave evolution is governed by a perturbed Korteweg–de Vries equation. In the absence of transverse variation, wave dispersion vanishes and the evolution equation reduces to a nonlinear advection equation with variable coefficients. As a general property of these equations, the total mass flux associated with the Kelvin wave is not conserved; residual mass must be generated. It is shown by an asymptotic analysis that this residual mass field is in balance with a mean geostrophic current long after the passage of the Kelvin wave. This result is verified using a numerical model. The physical mechanism evolved in the generation of the residual mass can be understood in terms of potential vorticity conservation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 303 - 324
Copyright
© 1991 Cambridge University Press

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References

Anderson, D. L. T. 1981 Cross-equatorial waves, with applications to the low-level east-African jet. Astrophys. Fluid Dyn. 16, 267–284.Google Scholar
Arakawa, A. & Lame, V. 1977 Computational design of the basic dynamical process of the CLA general circulation model. In Methods in Computational Physics, vol. 17, pp. 173–265. Academic.
Arakawa, A. & Lamb, V. 1981 A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Wea. Rev. 109, 18–36.Google Scholar
Blumen, W. 1972 Geostrophic adjustment. Rev. Geophys. Space Phys. 10, 485–528.Google Scholar
Gill, A. E. 1976 Adjustment under gravity in a rotating channel. J. Fluid Mech. 77, 603–621.Google Scholar
Gill, A. E. 1982 Atmosphere—Ocean Dynamics. Academic, 662 pp.
Grimshaw, R. 1977 Nonlinear aspects of long shelf waves. Geophys. Astrophys. Fluid Dyn. 8, 3–16. 324 P. ChangGoogle Scholar
Grimshaw, R. 1983 Solitary waves in slowly varying environments: long nonlinear waves. In Nonlinear Waves (ed. L. Debnath). Cambridge University Press, 360 pp.
Johnson, R. 1973 On the asymptotic solution of the Korteweg-de Vries equation with slowly varying coefficient. J. Fluid Mech. 60, 313–324Google Scholar
Kakutani, T. 1971 Effects of an uneven bottom on gravity waves. J. Phys, Soc. Japan 30, 272–276.Google Scholar
Killworth, P. D. 1989a How much of a baroclinic coastal Kelvin wave gets over a ridge? J. Phys. Oceanogr. 19, 321–341.Google Scholar
Killworth, P. D. 1989 Transmission of a two-layer coastal Kelvin wave over a ridge. J. Phys. Oceanogr. 19, 1131–1148.Google Scholar
Knickerbocker, C. J. & Newell, A. C. 1980 Shelves and the Korteweg-de Vries equation. J. Fluid Mech. 98, 803–818.Google Scholar
Knickerbocker, C. J. & Newell, A. C. 1985 Reflections from a solitary wave in a channel of varying depth. J. Fluid Mech. 153, 1–16.Google Scholar
Long, B. & Chang, P. 1990 Propagation of an equatorial Kelvin wave in a varying thermocline. J. Phys. Oceanogr. 20, 1826–1811.Google Scholar
Melville, W. K., Tomasson, G. G. & Renouard, D. P. 1989 On the stability of Kelvin waves. J. Fluid Mech. 206, 1–23.Google Scholar
Miles, J. W. 1972 Kelvin waves on oceanic boundaries. J. Fluid Mech. 55, 113–127.Google Scholar
Miles, J. W. 1973 Kelvin-wave diffraction by changes in depth. J. Fluid Mech. 57, 401–413.Google Scholar
Miles, J. W. 1979 On the Korteweg-de Vries equation for a gradually varying channel. J. Fluid Mech. 91, 181–190.Google Scholar
Newell, A. C. 1985 Solitons in Mathematics and Physics. Philadelphia, Pa: SIAM, pp. 244.
Rossby, C. G. 1937 On the mutual adjustment of pressure and velocity distributions in certain simple current systems. I. J. Mar. Res. 1, 15–28.Google Scholar
Rossby, C. G. 1938 On the mutual adjustment of pressure and velocity distributions in certain simple current systems. II. J. Mar. Res. 2, 239–263.Google Scholar
Smith, R. 1972 Nonlinear Kelvin and continental-shelf waves. J. Fluid Mech. 52, 379–391.Google Scholar