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An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 3. Free oscillations in natural basins

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

The extended channel model derived and analysed in two previous articles is further developed by investigating free oscillations and forced motion in natural enclosed basins. Firstly, a zeroth-order model is analysed. In this model, field variables are expressed as a product of a single known cross-sectional shape function and an unknown function of time and the co-ordinate along the lake axis. Conditions are discussed under which this zeroth-order model is meaningful, and it is shown that under normal circumstances Coriolis effects must be ignored. Subsequently the general Nth-order channel model is applied to the Lake of Lugano. It is shown that eigedrequencies and amphidromic systems are well predicted in such channel-like lakes. The paper ends with a discussion on the selection of shape functions and with further applications and limitations of the channel model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 283 - 299
Copyright
© 1982 Cambridge University Press

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References

Gary, J. & Helgason, R. 1970 A matrix method for ordinary differential equation eigenvalue problems. J. Comp. Phys. 5, 169–187.Google Scholar
Hamblin, P. F. 1972 Some free oscillations of a rotating natural basin. Ph.D. thesis, Univ. of Washington, Seattle.
Hamblin, P. F. 1976 Seiches, circulation and storm surges of an ice-free Lake Winnipeg. J. Fish. Res. Board 33, 2377–2391.Google Scholar
Neumann, G. 1944 Die Impedanz mechanischer Schwingungssysteme und ihre Anwendung auf die Theorie der Seiches. Ann. Hydr. Mar. Met. 72, 65–79.Google Scholar
Rao, D. B. 1966 Free gravitational oscillations in rotating rectangular basins. J. Fluid Mech. 25, 523–555.Google Scholar
Rao, D. B. 1973 Spectral methods of forecasting storm surges. Hydrological Sci. Bull. 18, 311–316.Google Scholar
Rao, D. B. 1977 Free internal oscillations in a narrow rotating rectangular basin. In Modeling of Transport Mechanisms in Oceans and Lakes (ed. T. S. Murty), pp. 391–398.
Rao, D. B. & Schwab, D. J. 1976 Two dimensional normal modes in arbitrary enclosed basins on a rotating Earth: application to Lakes Ontario and Superior. Phil. Trans. R. Soc. Lond. A 281, 63–96.Google Scholar
Raggio, G. 1981 A channel model for a curved elongated homogeneous lake. Dissertation, Eidgenössische Technische Hochschule Zürich. Mitteilung Nr 48 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zürich.
Raggio, G. 1982 On the Kantorovich technique applied to the tidal equations in elongated homogeneous lakes. J. Comp. Phys. (to appear).Google Scholar
Raggio, G. & Hotter, K. 1982a An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 1. Theoretical introduction. J. Fluid Mech. 121, 231–55.Google Scholar
Raggio, G. & Hutter, K. 1982b 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. J. Fluid Mech. 121, 257–281.Google Scholar
Schwab, D. J. 1978 Simulation and forecasting of Lake Erie storm surges. Mon. Weather Rev. 106, 1477–1487.Google Scholar
Scott, M. R. & Watts, H. A. 1975 A computer code for two-point boundary value problem via orthogonalization. Sandia Labs, Albuquerque SANDIA-75–0198.
Watts, H. A., Scott, M. R. & Lord, M. E. 1979 Solving complex valued differential systems. Sandia Labs, Alburquerque SANDIA-78–1501.Google Scholar