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Topographic waves in rectangular basins

Published online by Cambridge University Press:  21 April 2006

Thomas Stocker  and
Kolumban Hutter
Thomas Stocker
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, 8092-ETH Zürich, Switzerland
Kolumban Hutter
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, 8092-ETH Zürich, Switzerland
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Abstract

The channel model of Stocker & Hutter (1986, 1987) is used to construct topographic wave solutions in a rectangular basin on the f-plane with variable but symmetric bathymetry. We show that in a narrow period band three types of eigenmodes can be discerned which exhibit local, midscale and global structure, respectively. Wave motion can be trapped either at the long sides of the elongated basin (channel mode) or at the ends of it (bay mode) or alternatively, a basinwide phase rotation is observed (Ball mode). The new bay modes are explained as resonances of topographic wave reflection in a semi-infinite channel. The influence of the variation of the aspect ratio of the rectangle and the topography parameter on the wave periods is also investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 107 - 120
Copyright
© 1987 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
Bäuerle, E. 1986 Eine Untersuchung über topographische Wellen in einem Kanalmodell. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie. ETH Zürich, No. 83.
Finlayson, B. A. 1972 The Method of Weighted Residuals and Variational Principles. Academic.
Hutter, K., Salvadè, G. & Schwab, D. J. 1983 On internal wave dynamics in the northern basin of the Lake of Lugano. Geophys. Astrophys. Fluid Dyn. 27, 299–336.Google Scholar
Hutter, K. & Vischer, D. 1986 Lake Hydraulics. In Developments in Hydraulic Engineering (ed. P. Novak), vol. 4. Elsevier.
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: semi-infinite channels and elongated basins. J. Fluid Mech. 177, 395–405.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., Salvadè, G., Hutter, K. & Scheiwiller, T. 1985 Topographic waves in an elliptical basin, with application to the Lake of Lugano. Phil. Trans. R. Soc. A 316, 1–55.Google Scholar
Saylor, J. H., Huang, J. S. K. & Reid, R. O. 1980 Vortex modes in southern Lake Michigan. J. Phys. Oceanogr. 10, 1814–1823.Google Scholar
Stocker, T. 1987 A theoretical study of topographic wave reflection in estuaries. J. Phys. Oceanography (submitted).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. 1987 Topographic waves in channels and lakes on the f-plane. Lecture Notes on Coastal and Estuarine Studies, vol. 21. Springer.
Trösch, J. 1984 Finite element calculation of topographic waves in lakes. Proc. 4th Intl Conf. on Applied Numerical Modeling, Tainan, Taiwan.