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An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 2. First-order model applied to ideal geometry: rectangular basins with flat bottom

Published online by Cambridge University Press:  20 April 2006

Gabriel Raggio  and
Kolumban Hutter
Gabriel Raggio
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, The Federal Institute of Technology, Zurich, Switzerland
Kolumban Hutter
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, The Federal Institute of Technology, Zurich, Switzerland
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Abstract

A first-order channel model for fluid motion in long homogeneous lakes, as derived in detail by Raggio & Hutter (1982a), is presented. This model describes the motion through spatially one-dimensional boundary-value problems and is deduced by representing each field variable by cross-sectional expansions with a constant and a linear term. Various wave solutions of the governing equations applied to rectangular basins with flat bottom are presented. It is demonstrated that for moderate rotation speeds of the Earth and for elongated basins of a homogeneous fluid the main features of gravitational oscillations are predicted by the model. In particular Kelvin- and Poincaré-type waves are shown to exist. Furthermore, conditions of complete and incomplete reflections of Kelvin waves and free oscillations are discussed. The results corroborate the suitability of the model as far as wave motion in rectangular basins is concerned, but equally elucidate the physics behind them, which is less transparent when attacked with the full theory. The application of the model to basins of different shapes and to a real lake is reserved to a companion paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 257 - 281
Copyright
© 1982 Cambridge University Press

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References

Ball, F. K. 1965 The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid. J. Fluid Mech. 22, 529–545.Google Scholar
Chrystal, G. 1904 Some results in the mathematical theory of seiches. Proc. R. Soc. Edin. 25, 328–337.Google Scholar
Chrystal, G. 1905 Some further results in the mathematical theory of seiches. Proc. R. Soc. Edin. 25, 637–647.Google Scholar
Csanady, G. T. 1972 Response of large stratified lakes to wind. J. Phys. Oceanog. 2, 3–13.Google Scholar
Defant, F. 1953 Theorie der Corioliskraft. Arch. Met. Geophys. Biokl. (A) 6, 218–241.Google Scholar
Howard, L. N. 1960 Lectures on fluid dynamics. In Notes on the 1960 Summer Study Program in Geophysical Fluid Dynamics. Woods Hole, Mass. (ed. E. A. Spregel), vol. 1.
Hutter, K. & Raggio, G. 1982 A Chrystal-model describing gravitational barotropic motion in elongated lakes. Arch. Met. Geophys. Biokl. (to appear).
Johns, B. & Hamzah, A. M. O. 1969 On the seiche motion in a curved lake. Proc. Camb. Phil. Soc. 66, 607–615.Google Scholar
Kelvin, Lord 1879 On gravitational oscillations of rotating water. Proc. R. Soc. Edin. 10, 92–100.Google Scholar
Krauss, W. 1973 Methods and Results of Theoretical Oceanography, Part I, Dynamics of the Homogeneous and Quasihomogeneous Ocean. Berlin: Gebrueder Borntraeger.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Laplace, P. S. 1829 Mécanique Céleste 4, no. 1. Paris: Bachelier.
Leblond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.
Mortimer, C. H. 1963 Frontiers in physical limnology with particular reference to long waves in rotating basins. In Proc. 6th Conf. Great Lakes Res., Univ. Michigan, Great Lakes Res. Div. Publ. no. 10, pp. 9–42.
Pnueli, A. & Pekeris, C. L. 1968 Free tidal oscillations in rotating flat basins of the form of rectangles and sectors of circles. Proc. R. Soc. Lond. A 263, 149–171.Google Scholar
Poincaré, H. 1910 LeÇons de Mécanique Céleste 3, Théorie de Marées. Gauthier-Villars.
Raggio, G. 1981 A channel model for a curved elongated homogeneous lake. Dissertation, Eidgenoessische Technische Hochschule, Zurich. Mitteilungen Nr 49 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie ETH Zürich.
Raggio, G. & Hutter, K. 1982a An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 1. Theoretical introduction. J. Fluid Mech. 121, 231–255.Google Scholar
Raggio, G. & Hutter, K. 1982b An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 3. Free oscillations in natural basins. J. Fluid Mech. 121, 283–299.Google Scholar
Rao, D. B. 1966 Free gravitational oscillations in rotating rectangular basins. J. Fluid Mech. 25, 523–555.Google Scholar
Taylor, G. I. 1920 Tidal oscillations in gulfs and rectangular basins. Proc. Lond. Math. Soc. (2) 20, 148–181.Google Scholar