Abstract
By large scale circulation in lakes one means motions whose characteristic length scales extend over most parts or all of the water masses in a lake or the ocean. We present the governing equations and motivate, by means of a scale analysis, the various simplified versions of model equations that are in use in computational lake dynamics. This scale analysis not only permits rational deduction of the reduced equations, it equally provides a means of estimating their limitations. These are discussed as are the difficulties and the peculiarities inherent in the proposed equation sets.
Special features of external and internal wave motions are studied. For barotropic oscillations of a lake system (Lake of Lugano) it is shown that substantial water masses are exchanged between the individual basins at the resonating periods. Baroclinic seiches of a three layer model in which each layer is effective within its own domain show (for the North basin of the Lake of Lugano) that mode structures may differ from layer to layer pointing at important modifications of classical interpretations of higher baroclinic wave dynamics. And in large lakes in the equatorial belt theβ-effect forces modifications of the classical understanding of seiche behavior. Long periodic oscillating features may be attributed to topographic Rossby waves or higher baroclinic internal gravity waves; the observational identification is, however, difficult because lack of spatial resolution of the data makes this identification non-unique. We, finally present results of a full nonlinear numerical baroclinic circulation model and demonstrate that it is able to reproduce the gross features of the immediate response to strong storms during a few days.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anonymous, 1983, Hydrologische Messungen mit verankerten Instrumenten im Nordbecken des Luganersees während der Monate Juli/August 1979. Gemeinschaftsarbeit des Laboratorio di fisica Ferrestre, ICTS Lugano-Trevano, sowie der Gruppe “Physikalische Linologie” der VAW-ETH Zürich, Interner Bericht I/68, 328 pp.
Ball, F. K., 1965, Second class motions of a shallow liquid. J. Fluid Mech. 23:545–561.
Bäuerle, E., 1981, Die Eigenschwingungen abgeschlossener zweigeschichteter Wasserbecken bei variabler Bodentopographie. Dissertation an der Christian Alberts-Universität, Kiel, 79 pp.
Bührer, H. and A. H. Ambühl, 1975, Die Einleitung von gereinigtem Abwasser in Seen. Schweiz. Z. Hydrol. 37:347–369.
Charney, J. G., 1955, Generation of oceanic currents by wind. J. Mer. Res. 14:477–498.
Hollan, E. and T. J. Simons, 1978, Wind-induced changes of temperature and currents in Lake Constance, Arch. Met. Geophys. Biokl. Ser. A. 27:333–373.
Hutter, K., 1983, Strömungsdynamische Untersuchungen im Zürich- und im Luganersee. Ein Vergleich von Feldmessungen mit Resultaten theoretischer Modelle. Schweiz. Z. Hydrol. 45:101–144.
Hutter, K., 1984, Mathematische Vorhersage von barotropen und baroklinen Prozessen im Zürich und Luganersee. Vierteljahrschrift der Naturforschenden Gesellschaft in Zürich. 129:51–92.
Hutter, K., 1987, Hydrodynamic modeling of Lakes. Chapter 22 in: Encyclopedia of Fluid Mechanics (ed. Cheremesinoff), Gulf Publ. Com. Houston. 6:897–998.
Hutter, K., 1987, Schwingungen in einem Seensystem: Der Luganersee. Naturwissenschaften. 74:405–414.
Johnson, E. R., 1989, Topographic waves in open domains. Part 1. Boundary conditions and frequency estimates. J. Fluid Mech. 200:69–70.
Kielmann, J., 1981, Grundlagen und Anwendung eines numerischen Modells der geschichteten Ostsee. Bericht Inst. für Meereskunde, Kiel, No. 87 a, b.
Lemmin, U. and C. H. Mortimer, 1986, Tests of an extension to internal seiches of Defant's procedure for determination of surface seiche characteristics in real lakes. Limnol Oceanogr. 31:1207–1231.
Marchuk, G. I. and A. S. Sarkisyan, 1989, Mathematical Modeling of Ocean Circulation. Springer-Verlag Berlin etc., 292 pp.
Mortimer, C. H., 1952, Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere. Phil. Trans. R. Soc. London, 236 B:355–404.
Mortimer, C. H., 1974, Lake Hydrodynamics. Mitt. Internat. Verein. Limnol. 20:129–197.
Mortimer, C. H., 1979, Strategies for coupling data collection and analysis with dynamic modelling of lake motion. In: Lake Hydrodynamics, Symp. (W. H. Graf and C. H. Mortimer, Eds.). Elsevier, 183–277 E.
Mysak, L. A., 1980, Recent advances in shelf wave dynamics. Rev. Geophysics and Space Physics. 18:211–241.
Mysak, L. A., G. Salvade, K. Hutter and T. Scheiwiller, 1985, Topographic waves in a stratified elliptical basin, with application to the lake of Lugano. Phil. Trans. R. Soc. London 316:1–55.
Oman, G., 1982, Das Verhalten des geschichteten Zürichsees unter äußeren Windlasten. Mitt. No. 60 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der Eidgenössischen Technischen Hochschule, Zürich, 1–185.
Salvadè, G., C. Spinedi, F. Zamboni and K. Hutter, 1987, Baroclinic circulation in the stratified Southern basin of the Lake of Lugano (unpublished report)
Salvadè, G. and F. Zamboni, 1987, External gravity oscillations of the coupled basins of the Lake of Lugano. Annales Geophysicae. 5 B:247–254.
Salvadè, G., F. Zamboni and A. Barbieri, 1988, Three-Layer model of the North basin of the Lake of Lugano. Annales Geophysicae 6:463–474.
Simons, T. J., 1974, Verification of numerical models of Lake Ontario. I: Circulation in Spring and early Summer. J. Phys. Oceanogr. 4:507–523.
Simons, T. J., 1975, Verification of numerical models of Lake Ontario. II: Stratified circulations and temperature changes. J. Phys. Oceaonogr. 5:98–113.
Simons, T. J., 1976, Verification of numerical models of Lake Ontario. III: Long term heat transport. J. Phys. Oceanogr. 6:372–381.
Simons, T. J., 1978, Wind-driven circulations in the Southwest Baltic. Tellus 30:272–283.
Simons, T. J., 1980, Circulation models of lakes and inland seas. Can. Bull. Fisheries and Aquatic Sci. No. 203, 145 pp.
Stocker, T. and K. Hutter, 1986, One-dimensional models for topographic Rossby waves in elongated basins on thef-plane. J. Fluid Mech. 170:435–459.
Stocker, T. and K. Hutter, 1987a, Topographic waves in rectangular basins. J. Fluid Mech. 185:107–120.
Stocker, T. and K. Hutter, 1987b, Topographic Waves in Channels and Lakes on thef-plane. Lecture Notes on Coastal and Estuarine Studies. 21:173 pp.
Stocker, T. and E. R. Johnson, 1989, Topographic waves in open domains. Part 2: Bay modes and resonances. J. Fluid Mech. 200:77–93.
Stocker, T. and E. R. Johnson, 1989, Transmission and reflection of shelf waves by estuaries and headlands. J. Fluid Mech. (submitted).
Stocker, K., K. Hutter, G. Salvadè, J. Trösch and F. Zamboni, 1987, Observations and analysis of internal seiches in the Southern basin of Lake of Lugano. Annales Geophysicae 5 B:553–568.
Trösch, J., 1984, Finite element calculation of topographic waves in lakes. Proc. of Fourth Int. Conf. on Applied Numerical Modeling, Taiwan.
Author information
Authors and Affiliations
Additional information
This paper is an extended version of a lecture with the same title, held by K. Hutter on June 14, 1989, at the Workshop “Spatial and temporal scales of water bodies” of the Sonderforschungsbereich “Stoffhaushalt des Bodens”, Universität Konstanz. The character of the paper is that of areview, however, it contains material, theoretical, computational and observational, that has never been presented before to make it sufficiently unique. Some of the new material has been collected and gathered by E. Bäuerle, G. Salvadè, C. Spinedi and F. Zamboni, who should be credited for it, even though none of these people contributed to the layout and drafting of the text, for which K. Hutter is responsible alone.
We thank Professor Max Tilzer of the University Konstanz for inviting K. Hutter to the workshop and giving him the opportunity to present the material as of that time.
As far as referencing current literature is concerned we are neither exhaustive nor complete and only refer to literature which is directly related to the material presented. For a list with more than 300 relevant references, the reader may consult the article “Hydrodynamic Modeling of Lakes” by K. Hutter in the Encyclopedia of Fluid Mechanics, Gulf Publ. Company, Houston Texas (1987). I would like to express my sincere thanks to Mrs. Danner for her diligent work in typing the text.
Rights and permissions
About this article
Cite this article
Hutter, K., Salvadè, G., Spinedi, C. et al. Large scale water movements in lakes. Aquatic Science 53, 100–135 (1991). https://doi.org/10.1007/BF00877057
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00877057