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The response of lake levels to an unsteady wind stress

Published online by Cambridge University Press:  17 April 2009

B.J. Noye
B.J. Noye
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia.
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Abstract

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This paper presents a theoretical investigation into the forced oscillations produced in an elongated lake by wind stresses varying in time. Analysis of the appropriate hydrodynamical equations of motion, in the absence of friction, and the equation of continuity give an estimate of the response function of the longitudinal component of the wind stress onto water level. Two mathematical models are used, one giving an analytical solution and the other requiring numerical methods for solution. The first model assumes that the lake is a homogeneous rectangular body of water and the second uses the mean depth h(x) and area of cross section A(x), considered as functions of distance x directed along the longitudinal axis of the lake.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 423 - 433
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Babuška, Ivo, Práger, Milan and Vitásek, Emil (in cooperation with R. Radok), Numerical processes in differential equations (SNTL, Prague; Interscience [John Wiley & Sons], London, New York, Sydney; 1966).Google Scholar
[2]Haurwitz, B., The slope of lake surfaces under variable wind stresses (Technical Memorandum No. 25; Beach Erosion Board, 1951).Google Scholar
[3]Hellström, B., Wind effect on lakes and rivers (IngvetenskAkad. Handl. 158, Stockholm, 1941).Google Scholar
[4]Keulegan, Garbis H., “Wind tides in small closed channels”, J. Res. Nat. Bur. Standards 46 (1951), 358–381.CrossRefGoogle Scholar
[5]Kreyszig, Erwin, Advanced engineering mathematics, 2nd ed. (John Wiley & Sons, New York, London, Sydney, 1967).Google Scholar
[6]Langhaar, H.L., “Wind tides in inland waters”, Proc. First Midwest. Conf. Fluid Dynam., May 1950, 278–296.(J.W. Edwards, Ann Arbor, Michigan, 1951).Google Scholar
[7]Proudman, J., Dynamical oceanography (Methuen, London; John Wiley & Sons, New York; 1953).Google Scholar
[8]Saito, Y., “A solution to the oscillation of lake water generated by wind” (Japanese), J. Meteor. Soc. Japan (2) 27 (1949), 20–25.CrossRefGoogle Scholar
[9]Saville, T. Jr, Wind set-up and waves in shallow water (Technical Memorandum No. 27; Beach Erosion Board, 1952).Google Scholar
[10]Tareyev, B.A., “Stationary wind set up and circulation in a shallow rectangular basin”, Bull. (Izv.) Acad. Sci. USSR, Geophys. Ser. 1958, 661–663.Google Scholar
[11]Van Dorn, William G., “Wind stress on an artificial pond”, J. Mar. Res. 12 (1953), 249–276.Google Scholar