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The low-frequency scattering of Kelvin waves by stepped topography

Published online by Cambridge University Press:  26 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

A straightforward method that yields explicit transmission amplitudes is presented for Kelvin wave scattering by topography whose isobaths are parallel sufficiently far from the vertical, but not necessarily planar, wall supporting the incident wave. These results are obtained by first restricting attention to the low-frequency limit in which the flow splits naturally into three regions: an outer-x region containing the incident and transmitted Kelvin waves, an outer-y region containing outwardly propagating long topographic waves and an inner quasi-steady geostrophic region whose structure follows from earlier time-dependent analyses. The present analysis is further simplified by approximating general smooth features by stepped profiles with no restriction on the size, number or order of steps. Various qualitative results on the transmission amplitudes and flow fields are deduced from the explicit solutions and results are given on orthogonality, completeness and direction of propagation of the scattered long waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 23 - 44
Copyright
© 1990 Cambridge University Press

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References

Gill, A. E., Davey, M. K., Johnson, E. R. & Linden, P. F. 1986 Rossby adjustment over a step. J. Mar. Res. 44, 713–738.Google Scholar
Golub, G. H. & Van Loan, C. F. 1983 Matrix Computations, Chapter 7. North Oxford Academic.
Huthnance, J. M. 1975 On trapped waves over a continental shelf. J. Fluid Mech. 69, 689–704.Google Scholar
Johnson, E. R. 1985 Topographic waves and the evolution of coastal currents. J. Fluid Mech. 160, 499–509.Google Scholar
Johnson, E. R. 1989a Boundary currents, free currents and dissipation regions in the low-frequency scattering of shelf waves. J. Phys. Oceanogr. 19, 1293–1302.Google Scholar
Johnson, E. R. 1989b Connection formulae and classification of scattering regions for low-frequency shelf waves. J. Phys. Oceanogr. 19, 1303–1312.Google Scholar
Johnson, E. R. 1989c The scattering of shelf waves by islands. J. Phys. Oceanogr. 19, 1313–1318.Google Scholar
Johnson, E. R. 1989d Topographic waves in open domains. Part 1. Boundary conditions and frequency estimates. J. Fluid Mech 200, 69–76.Google Scholar
Johnson, E. R. 1990a Energy conservation in low-frequency scattering of shelf-waves. J. Phys. Oceanogr. (submitted).Google Scholar
Johnson, E. R. 1990b Kelvin wave scattering and long waves over smooth topography. J. Fluid Mech. (submitted) (referred to as II).Google Scholar
Johnson, E. R. & Davey, M. K. 1990 Free surface adjustment and topographic waves in coastal currents. J. Fluid Mech. (in press).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. 1989b On the transmission of a two-layer coastal Kelvin wave over a ridge. J. Phys. Oceanogr. 19, 1131–1148.Google Scholar
Longuet-Higgins, M. S. 1968 Double Kelvin waves with continuous depth profiles. J. Fluid Mech. 34, 49–80.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
Taylor, G. I. 1921 Tidal oscillations in gulfs and rectangular basins. Proc. Lond. Math. Soc. 20, 148–181.Google Scholar
Thomson, W. 1879 On gravitational oscillations of rotating water. Proc. R. Soc. Edinburgh 10, 92–100.Google Scholar