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The trapping and scattering of topographic waves by estuaries and headlands

Published online by Cambridge University Press:  26 April 2006

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

This paper extends recent theoretical work on sub-inertial trapped modes in bays to consider trapping of energy in the neighbourhood of estuary mouths on coastal shelves. The qualitative form of the theoretical predictions accords well with recent observations on the Scotian Shelf that show energy trapped near the Laurentian Channel at a frequency higher than that of the propagating waves on the shelf.

The trapping and scattering of shelf waves is modelled for a shelf–estuary or shelf–headland system by considering barotropic waves in a straight, infinite channel with an attached rectangular estuary or interrupted by a rectangular headland. Taking the depth to increase exponentially with distance from the coast and expanding in cross-shelf modes reduces the problem to a system of real linear algebraic equations.

Trapped modes with frequencies above the cutoff frequency of propagating waves are found near the mouth of the estuary. Waves propagating towards the estuary are strongly scattered and, for particular frequencies, incident energy can be either perfectly transmitted or totally reflected. An incident wave can be in resonance with the estuary causing energy to penetrate the estuary. Bounds on the frequencies of trapped and resonant solutions are given and allow an easy modal interpretation.

If the frequency of an incident wave is sufficiently high, waves cannot propagate past a headland. Energy at these frequencies can however tunnel through the region and appear as an attenuated wave on the far side. For particular frequencies all energy passes the headland and none is reflected. For headlands long compared with the incident wave, transmission coefficients for single-mode scattering follow from spatially one-dimensional wave mechanics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 501 - 524
Copyright
© 1991 Cambridge University Press

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References

Buchwald, V. T. & Adams, J. K., 1968 The propagation of continental shelf waves. Proc. R. Soc. Lond. A 305, 235–250.Google Scholar
Buchwald, V. T. & Williams, N. V., 1975 Rectangular resonantors on infinite and semi-infinite channels. J. Fluid Much. 67, 497–511.Google Scholar
Davis, A. M. J.: 1983 Shelf-similar topographies for free continental shelf waves. Geophys. Astrophys. Fluid Dyn. 23, 321–331.Google Scholar
Grimshaw, R.: 1977 The effects of a variable Coriolis parameter, coastline curvature and variable bottom topography on continental shelf waves. J. Phys. Oceanogr. 7, 547–554.Google Scholar
Huthnance, J. M.: 1978 On coastal trapped waves: analysis and numerical calculation by inverse iteration. J. Phys. Oceanogr. 8, 74–92.Google Scholar
Johnson, E. R.: 1987 A conformal-mapping technique for topographic-wave problems: semi-infinite channels and elongated basins. J. Fluid Mech. 177, 395–405.Google Scholar
Johnson, E. R.: 1989a Topographic waves in open domains. Part 1. Boundary conditions and frequency estimates. J. Fluid Mech. 200, 69–76.Google Scholar
Johnson, E. R.: 1989b Boundary currents, free currents and dissipation in the low-frequency scattering of shelf waves. J. Phys. Oceanogr. 19, 1291–1300.Google Scholar
Johnson, E. R.: 1989c Connection formulae and classification of scattering regions for low-frequency shelf waves. J. Phys. Oceanogr. 19, 1301–1310.Google Scholar
Johnson, E. R.: 1990 Low-frequency barotropic scattering on a shelf bordering an ocean. J. Phys. Oceanogr. (in press).Google Scholar
Landau, L. D. & Lifshitz, E. M., 1965 Quantum Mechanics, Course in Theoretical Physics, vol. 3, Pergamon, 616 p.
Lighthill, M. J.: 1958 An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.
Mysak, L. A.: 1980 Recent advances in shelf wave dynamics. Rev. Geophys. Space Phys. 18, 211–241.Google Scholar
Middlbton, J. H., Foster, T. D. & Foldvik, A., 1987 Diurnal shelf waves in the southern Weddell Sea. J. Phys. Oceanogr. 17, 784–791.Google Scholar
Middleton, J. H. & Wright, D. G., 1988 Shelf wave scattering due to a longshore jump in topography. J. Phys. Oceanogr. 18, 230–242.Google Scholar
Schwing, F. B.: 1989 Subtidal response of the Scotian Shelf bottom pressure field to meteorological forcing. Atmos. Ocean 27, 157–180.Google Scholar
Stocker, T.: 1988 A numerical study of topographic wave reflection in semi-infinite channels. J. Phys. Oceanogr. 18, 609–618.Google Scholar
Stocker, T. & Hutter, K., 1987 Topographic waves in rectangular basins. J. Fluid Mech. 185, 107–120.Google Scholar
Stocker, T. F. & Johnson, E. R., 1989 Topographic waves in open domains. Part 2. Bay modes and resonances. J. Fluid Mech. 200, 77–93.Google Scholar
Webster, I.: 1987 Scattering of coastally trapped waves by changes in continental shelf width. J. Phys. Oceanogr. 17, 928–937.Google Scholar
Wilkin, J. L. & Chapman, D. C., 1987 Scattering of continental shelf waves at a discontinuity in shelf width. J. Phys. Oceanogr. 17, 713–724.Google Scholar