Higher-Order Baroclinicity (II)Interpretation of Lake Data with Rotating and Non-rotating Models

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM, volume 2)


In parts A and B of the last chapter, two sources of higher order baroclinicity were looked at (1) a two-layer fluid system with a diffusive interface and (2) a three-layer configuration with two sharp interfaces due to the presence of a thermocline and a chemocline. In this chapter we give further field evidences of higher order baroclinicity. Both cases are to a certain extent idealized; in a realistic situation, density changes are generally less abrupt and should be represented by using a thermal equation of state ρ = ρ(T, s) from measured temperature and electrical conductivity profiles. If this argument is consistently adopted, this would, strictly, mean that a numerical model for a stratified lake should be based on a multi-layer model, e.g. with linear density variation across each layer. For reasons of accurate determination of the phase speeds of the higher baroclinic seiche, this should be done so, even if only fundamental (V1) and first higher order (V2) modes are of interest.


Internal Wave Phase Speed Baroclinic Mode South Basin Main Basin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Antenucci, J.P. and Imberger, J.: Energetics of long internal gravity waves in large lakes. Limnol. Oceanogr. 46(7), 1760–1773 (2001)Google Scholar
  2. 2.
    Antenucci, J.P. and Imberger, J.: On internal waves near the high-frequency limit in an enclosed basin. J. Geophys. Res, 106, C10, 22465–22474 (2001)Google Scholar
  3. 3.
    Antenucci, J.P., Imberger, J. and Saggio, A.: Seasonal evolution of the basin-scale internal wave field in a large stratified lake. Limnol. Oceanogr., 45, 1621–1638 (2000)CrossRefGoogle Scholar
  4. 4.
    Appt, J., Imberger, J. and Kobus, H.: Basin-scale motion in stratified Upper Lake Constance. Limnol. Oceanogr., 49(4), 919–933 (2004)CrossRefGoogle Scholar
  5. 5.
    Barrondale, I. and Erickson, R.: Algorithms for least-squares linear prediction and maximum entropy spectral analysis. Part 2: Fortran Program. Geophysics, 45, 433–446 (1980)Google Scholar
  6. 6.
    Bauer, G., Diebels, S. and Hutter, K.: Nonlinear internal waves in ideal rotating basins. Geophys. Astrophys. Fluid Dyn., 78, 21–46 (1994)CrossRefGoogle Scholar
  7. 7.
    Bäuerle, E.: Die Eigenschwingungen abgeschlossener, zweigeschichteter Wasserbecken mit variabler Topographie. Berichte aus dem Institut für Meereskunde, Kiel, 85, 126p (1981)Google Scholar
  8. 8.
    Bäuerle, E.: Internal free oscillations in the Lake of Geneva. Ann. Geophysicae, 3, 199–206 (1985)Google Scholar
  9. 9.
    Bäuerle, E.: Transverse baroclinic oscillations in Lake Überlingen. Aquatic Sci., 56, 145–160 (1994)CrossRefGoogle Scholar
  10. 10.
    Bäuerle, E., Ollinger, D. and Ilmberger, J.: Some meteorological, hydrological, and hydrodynamical aspects of Upper Lake Constance. Arch. Hydrobiol. Sopec. Issues Adv. Limnol., 53, 31–83 (1998)Google Scholar
  11. 11.
    Boegman, L. Imberger, J. Ivey, G.N. and Antenucci, J.P.: High-frequency internal waves in large stratified lakes. Limnol.Oceanogr., 48(2), 895–919 (2003)Google Scholar
  12. 12.
    Boegman, L. Ivey, G.N. and Imberger, J.: The energetics of large-scale internal wave degeneration in lakes. J. Fluid. Mech., 531, 159–180 (2005)CrossRefGoogle Scholar
  13. 13.
    Casulli, V. and Cattani, E.: Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow. Comput. Math. Applic., 27, 99–112 (1994)CrossRefGoogle Scholar
  14. 14.
    Casulli, V. and Cheng, R.T.: Semi-implicit finite difference method for three- dimensional shallow water flow. Int. J. Numerical Methods Fluids, 15, 629–648 (1992)CrossRefGoogle Scholar
  15. 15.
    Goldstein, S.: Tidal motion in rotating elliptical basins of constant depth. Monthly Notices R. Atron. Soc. (Geophys. Supp.), 2, 213–231 (1929)Google Scholar
  16. 16.
    Gloor, M., Wüest, A. and Münnich, M.: Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiologia, 284, 59–68 (1994)CrossRefGoogle Scholar
  17. 17.
    Heaps, N.S.: Seiches in a narrow lake, uniformly stratified in three layers. Geophys. Suppp. R. Astron. Soc., 5, 134–156 (1961)CrossRefGoogle Scholar
  18. 18.
    Heaps, N.S.: Development of a three-layered spectral model for the motion of a stratified shelf sea. I. Basic equations. In:Physical Oceanography of Coastal and Shelf Seas (ed.: B. Johns). Amsterdam Elsevier, 386–400 (1983)Google Scholar
  19. 19.
    Heaps, N.S.: Development of a three-layered spectral model for the motion of a stratified shelf sea. II. Experiments with a rectangular basin representing the Celtic Sea. In: Physical Oceanography of Coastal and Shelf Seas (ed.: B. Johns). Amsterdam Elsevier, 401–465 (1983)Google Scholar
  20. 20.
    Heinz, G.: Strömungen im Bodensee. Ergebnisse einer Messkampagne im Herbst 1993. Mitt. Versuchsanstalt für Wasserbau, Hydrologie & Glaziologie an der ETH Zürich (Ed.: D. Vischer), 135 (1995)Google Scholar
  21. 21.
    Hodges, B.R. and Dallimore, C.J.: Estuary and lake computer model. ELCOM scence manual code (Version 1.5.) Centre for Water Research, University of Western Australia (2001)Google Scholar
  22. 22.
    Hodges, B.R., Imberger, J., Saggio, A. and Winters, K.B.: Modeling basin-scale internal waves in a stratified lake. Limnol. Oceanogr., 45(4), 1603–1620 (2000)CrossRefGoogle Scholar
  23. 23.
    Hollan, E.: Wind-induced motions in Lake Constance. Bericht der AWBR, 6, 111–187 (1974)Google Scholar
  24. 24.
    Horn, W., Mortimer, C.H. and Schwab, D.J.: Wind-induced internal seiches in the Lake of Zürich observed and modelled. Limnol. Oceanogr., 31(6), 1230–1252 (1986)CrossRefGoogle Scholar
  25. 25.
    Huss, E. and Stranz, D.: die Windverhältnisse am Bodensee. Pure, Appl. Geophys., 81, 323–56 (1970)Google Scholar
  26. 26.
    Hutter, K., Salvadè, G. and Schwab, D.J.: On internal wave dynamics in the Northern Basin of the Lake of Lugano. Geophys. Astrophys. Fluid Dyn., 27, 299–336 (1983)CrossRefGoogle Scholar
  27. 27.
    Hutter, K., Bauer, G., Wang, Y. and Güting, P.: Forced motion response in enclosed lakes. In: Amer. Geophys. Union, Coastal and Estuarine Studies. Physical Processes in Lakes and Oceans (Ed.: J. Imberger), 54, 137–166 (1998)Google Scholar
  28. 28.
    Jeffreys, H.: The free oscillations of water in an elliptical lake. Proc. Lond. Math. Soc., 23, 455–476 (1925)CrossRefGoogle Scholar
  29. 29.
    Kanari, S.: The long internal waves in Lake Biwa. Limnol. Oceanogr., 20, 544–553 (1975)CrossRefGoogle Scholar
  30. 30.
    LaZerta, B.D.: The dominating higher order vertical modes of the internal seiche in a small lake. Limnol.Oceanogr., 25(5), 846–854 (1980)Google Scholar
  31. 31.
    Laval, B., Imberger, J., Hodges, B.R. and Stocker, R.: Modeling circulation in lakes: Spatial and tempral variations. Limnol. Oceanogr., 48(3), 983–994 (2003)CrossRefGoogle Scholar
  32. 32.
    LeBlond, P.H. and Mysak, L.A.: Waves in the Ocean. Elsevier Oceanogr. Ser., Elsevier Scientific Publ. Co., Amsterdam, Oxford. New York (1978, 1980)Google Scholar
  33. 33.
    Lemmin, U. and Mortimer, C.H.: Tests of an extension to internal seiches of Defant’s procedure for determination of surface seiche characteristics in real lakes. Limnol. Oceanogr., 31(6), 1207–1231 (1986)CrossRefGoogle Scholar
  34. 34.
    Lemmin, U., Mortimer, C.H. and Bäuerle, E.: Internal seiche dynamics in Lake Geneva. Limnol. Oceanogr., 50(1), 207–216 (2005)CrossRefGoogle Scholar
  35. 35.
    MacIntire, S., Flynn, K.M., Jellison, R. and Romero, J.R.: Boundary mixing and nutrient fluxes in Mono Lake, California. Limnol. Oceanogr., 44, 512–529 (1999)CrossRefGoogle Scholar
  36. 36.
    Mortimer, C.H.: The resonant responses of stratified lakes to wind. Schweiz. Z. Hydrol., 15, 94–151 (1953)Google Scholar
  37. 37.
    Mortimer, C.H.: Lake Hydrodynamics. Mitt. Int. V. Theor. Angew. Limnol., 20, 124–197 (1974)Google Scholar
  38. 38.
    Mortimer, C.H.: Strategies for coupling data collection and analysis with the dynamic modeling of lake motions. In: Lake Hydrodynamics (Eds. W.H. Graf and C.H. Mortimer), Elsevier, Amsterdam, 183–222E (1979)Google Scholar
  39. 39.
    Mortimer, C.H.: Lake Michigan in Motion. Responses of an Inland Sea to Weather, Earth-Spin, and Human Activities. The University of Wisconsin Press, 311 pp (2004)Google Scholar
  40. 40.
    Mühleisen, R.: Starkwinde an und auf dem Bodensee. Meteorol. Rundschau, 30, 15–22 (1977)Google Scholar
  41. 41.
    Münnich, M., Wüest, A. and Imboden, D.M.: Observations of the second vertical mode of the internal seiche in an alpine lake. Limnol. Oceanogr., 37(8), 1705–1719 (1992)CrossRefGoogle Scholar
  42. 42.
    Ogihara, Y.: Internal Wave Energy Distribution. Ph. D. Thesis, University of Western Australia (1998)Google Scholar
  43. 43.
    Ollinger, D.: Modellierung von Temperatur, Turbulenz und Algenwachstum mit einem gekoppelten physikalisch-biologischen Modell. Doctoral Disseratation, Ruprechts-Karls Univertiät Heidelberg (1999)Google Scholar
  44. 44.
    Roget, E.: Internal Seiches and Baroclinic Currents in Lake Banyoles. Ph. D. Thesis, Autonomous University, Barcelona, 287p (1992)Google Scholar
  45. 45.
    Roget, E., Salvadè, G. and Zamboni, F.: Internal seiche climatology in a small lake where transversal and second vertical modes are usually observed. Limnol.Oceanogr., 42(4), 663–673 (1997)Google Scholar
  46. 46.
    Saggio, A. and Imberger, J.: Internal wave weather in a stratified lake. Limnol. Oceanogr., 43(8), 1780–1795 (1998)Google Scholar
  47. 47.
    Schimmele, M.: Anregung interner Seiches im Bodensee durch den Wind. Doctoral dissertation, Ruprecht-Karls Universität Heidelberg (1993)Google Scholar
  48. 48.
    Serruya, S., Hollan, E. and Bitsch B.: Steady winter circulation in Lakes Constance and Kinneret driven by wind and main tributaries. Archiv für Hydrobiologie, Suppl. 70(1), 33–110 (1984)Google Scholar
  49. 49.
    Stocker, K., Hutter, K., Salvadè, G., Trösch, J. and Zamboni, F.: Observations and analysis of internal seiches in the Southern Basin of Lake of Lugano. Ann Geophysicae, 5B, 553–568 (1987)Google Scholar
  50. 50.
    Shimizu, K., Imberger, J. and Kumagai, M.: Horizontal structure and excitation of primary motions in a strongly stratified lake. Limnol. Oceanogr., 52(6), 2641–2655 (2007)CrossRefGoogle Scholar
  51. 51.
    Damping mechanisms of internal waves in continuously stratified rotating basins. J. Fluid. Mech. 637, 137–172 (2009)Google Scholar
  52. 52.
    Shimizu, K. and Imberger, J.: Energetics and damping of basin-scale internal waves in a strongly stratified lake. Limnol. Oceanogr., 53(4), 1574–1588 (2008)CrossRefGoogle Scholar
  53. 53.
    Trampe, J.: Principles of analog and digital frequency analysis. Norwegian Institute of Technology (1981)Google Scholar
  54. 54.
    Wiegand, R.C. and Chamberlain, V.: Internal waves of the second vertical mode in a stratified lake. Limnol. Oceanogr. 32(1), 29–42 (1987)Google Scholar
  55. 55.
    Wang, Y., Hutter, K. and Bäuerle, E.: Wind-induced baroclinic response of Lake Constance. Annales Geophysicae, 18, 1488–1501 (2000)CrossRefGoogle Scholar
  56. 56.
    Zenger, A., Anker, W., Ilmberger, J. and Münnich, K.-O.: Die Untersuchungen der Windverhältnisse im westlichen Teil des Bodensees und die Untersuchung von Landwinden auf Seebedingungen. Meteorol. Rundschau., 42, 42–51 (1990)Google Scholar
  57. 57.
    Zenger, A., Ilmberger, J., Heinz, G., Schimmele, M. and Münnich, K.-O.: Struktur der internen Seiches des Bodensees. Wasserwirtschaft, 79, 616–623 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.c/o Versuchsanstalt für Wasserbau Hydrologie und Glaziologie ETH-ZentrumETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.P.P. Shirshov Institute of OceanologyRussian Academy of SciencesKaliningradRussia

Personalised recommendations