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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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