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Topographic waves in open domains. Part 2. Bay modes and resonances

Published online by Cambridge University Press:  26 April 2006

Thomas F. Stocker  and
E. R. Johnson
Thomas F. Stocker
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zürich, Switzerland.
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

The topographic wave equation is solved in a domain consisting of a channel with a terminating bay zone. For exponential depth profiles the problem reduces to an algebraic eigenvalue problem. In a flat channel adjacent to a shelf–like bay zone the solutions form a countably infinite set of orthogonal bay modes: the spectrum of eigenfrequencies is purely discrete. A channel with transverse topography allows wave propagation towards and away from the bay: the spectrum has a continuous part below the cutoff frequency of free channel waves. Above this cutoff frequency a finite number (possibly zero) of bay-trapped solutions occur. Bounds for this number are given. At particular frequencies below the cutoff the system is in resonance with the incident wave. These resonances are shown to be associated with bay modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 77 - 93
Copyright
© 1989 Cambridge University Press

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References

Ball, F. K.: 1965 Second class motions of a shallow liquid. J. Fluid Mech. 23, 545–561.Google Scholar
Johnson, E. R.: 1987a Topographic waves in elliptical basins. Geophys. Astrophys. Fluid Dyn. 37, 279–295.Google Scholar
Johnson, E. R.: 1987b A conformal mapping technique for topographic wave problems: semiinfinite channels and elongated basins. J. Fluid Mech. 177, 395–405.Google Scholar
Johnson, E. R.: 1989 Topographic waves in open domains. Part 1: Boundary conditions and frequency estimates. J. Fluid Mech. 200, 69–76.Google Scholar
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Mysak, L. A.: 1985 Elliptical topographic waves. Geophys. Astrophys. Fluid Dyn. 31, 93–135.Google Scholar
Mysak, L. A., Salvade, G., Hutter, K., Scheiwiller, T.: 1985 Topographic waves in an elliptical basin, with application to the Lake of Lugano. Phil. Trans. R. Soc. Lond. A 316, 1–55.Google Scholar
Rhines, P. B.: 1969a Slow oscillations in an ocean of varying depth. Part 1. Abrupt topography. J. Fluid Mech. 37, 161–189.Google Scholar
Rhines, P. B.: 1969b Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–205.Google Scholar
Rhines, P. B. & Bretherton, F., 1973 Topographic Rossby waves in a rough–bottomed ocean. J. Fluid Mech. 61, 583–607.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., 1986 One-dimensional models for topographic Rossby waves in elongated basins on the f-plane. J. Fluid Mech. 170, 435–459.Google Scholar
Stocker, T. & Hutter, K., 1987a Topographic Waves in Channels and Lakes on the f-Plane. Lecture Notes on Coastal and Estuarine Studies, Vol. 21. Springer.
Stocker, T. & Hutter, K., 1987b Topographic waves in rectangular basins. J. Fluid Mech. 185, 107–120.Google Scholar
Trösch, J.: 1984 Finite element calculation of topographic waves in lakes. Proc. 4th Intl Conf. Appl. Numerical Modeling. Tainan, Taiwan (ed. Han Min Hsia, You Li Chou, Shu Yi Wang & Sheng Jii Hsieh), pp. 307–311.