Advertisement

Linear Gravity Waves, Kelvin Waves and Poincare Waves, Theoretical Modelling and Observations

  • Kolumban Hutter
Part of the International Centre for Mechanical Sciences book series (CISM, volume 286)

Abstract

Waves in lakes are primarily generated by external meteorological forces. The latter are complex in their spatial and temporal structure and thus impose a large spectrum of the typical physical scales. Their explanation and relation to the primary cause is one of the principal goals of physical limnology.

Keywords

Gravity Wave Internal Wave Baroclinic Mode Surface Gravity Wave Equivalent Depth 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bauer, S.W., Graf, W.H., Mortimer, C.H. and Perrinjaquet, C., 1981. Inertial Motion in Lake Geneva (Le Léman). Arch. Met. Geoph. Biokl., Ser. A, 30, pp. 283–312.Google Scholar
  2. Bäuerle, E., 1981. Die Eigenschwingungen abgeschlossener, zwei-geschichteter Wasserbecken bei variabler Bodentopographie. Dissertation an der Christian Alberts Universität, Kiel.Google Scholar
  3. Brown, P.J., 1973. Kelvin wave reflection in semi-infinite canal. J. Mar. Res., Vol. 31, pp. 1–10.Google Scholar
  4. Courant, R. and Hilbert, D., 1982. Methods of Mathematical Physics. Vol. 1, Interscience Publ. John Wiley & Sons, New York.Google Scholar
  5. Csanady, G.T. and Scott, J.T., 1974. Baroclinic coastal jets in Lake Ontario during IFYGL. J. Phys. Oceanogr., Vol. 4, pp. 524–541.CrossRefADSGoogle Scholar
  6. Defant, A., 1961. Physical Oceanography. Oxford University Press, Oxford.Google Scholar
  7. Defant, F., 1953. Theorie der Seiches des Michigansees und ihre Abwandlung durch Wirkung der Corioliskraft. Arch. Met. Geophys. Biokl., Ser. A, Vol. 6, pp. 218–241.CrossRefGoogle Scholar
  8. Finlayson, B.A., 1972. The method of weighted residuals and variational principles. Academic Press, New York.MATHGoogle Scholar
  9. Forel, A.F., 1895. Le Léman. Monographie, Limnologie, tome 1 &2. Ed. F. Rouge Librairie de l’Université, Lausanne.Google Scholar
  10. Greenspan, H.P., 1968. The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
  11. Hamblin, P.F., 1974. Short period tides in Lake Ontario. Proc. 17th Conf. Great Lakes Res. Internat. Assoc. Great Lakes Res., pp. 789–800.Google Scholar
  12. Hamblin, P.F., 1976. A theory of short period tides in a rotating basin. Phil. Trans. Royal Soc. London, Vol. A291, pp. 97–111.Google Scholar
  13. Hamblin, P.F., 1978. Internal Kelvin waves in a fjord lake. J. Geophys. Res., Vol. 83, pp. 287–300.Google Scholar
  14. Hamblin, P.F. and Hollan, E., 1978. On the gravitational seiches of Lake Constance and their generation. Schweiz. Z. Hydr., Vol. 40, pp. 119–154.Google Scholar
  15. Hayes, W.H., 1974. Introduction to wave propagation. In: Nonlinear Waves (ed. by S. Leibovich & A.R. Seebass ). Cornell University Press, Ithaca, London.Google Scholar
  16. Heaps, N.S., 1961. Seiches in a narrow lake, uniformly stratified in three layers. Geophys. Suppl. J. Roy. Astron. Soc., Vol. 5, pp. 134–156.CrossRefMATHGoogle Scholar
  17. Hollan, E., 1979. Hydrodynamische Modellrechnungen über die Eigenschwingungen des Bodensee-Obersees mit einer Deutung des Wasserwunders von Konstanz im Jahre 1949. Schw. Verein für Geschichte des Bodensees und seiner Umgebung, Heft 97, pp. 157–192.Google Scholar
  18. Hollan, E., 1980. Die Eigenschwingungen des Bodensee-Obersees und eine Deutung des “Wasserwunders von Konstanz” im Jahre 1549. Deutsches gewässerkundliches Jahrbuch, ISSN 0344–0788, Abflussjahr 1979.Google Scholar
  19. Hollan, E., Rao, D.B. and Bäuerle, E., 1980. Free surface oscillations in Lake Constance with an interpretation of the “Wonder of the rising water at Konstanz” 1549. Arch. Met. Geophys. Biokl., Ser. A, Vol. 29, pp. 301–325.CrossRefGoogle Scholar
  20. Horn, W., Mortimer, C.H. and Schwab, D.J., 1983. Internal wave dynamics of the Lake of Zurich, preprint.Google Scholar
  21. Rutter, K. and Raggio, G., 1982. A Chrystal-model describing gravitational barotropic motion in elongated lakes. Arch. Met. Geophys. Biokl., Ser. A, Vol. 31, pp. 361–378.CrossRefGoogle Scholar
  22. Hutter, K. and Schwab, D.J., 1982. Baroclinic channel models. Internal report No. 62, Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich.Google Scholar
  23. Hutter, K., Raggio, G., Bucher, C. and Salvadè, G., 1982a. The surface seiches of Lake of Zurich. Schweiz. Z. Hydr., Vol. 44, pp. 423454.Google Scholar
  24. Hutter, K., Raggio, G., Bucher, C., Salvadè, G. and Zamboni, F., 1982b. The surface seiches of the Lake of Lugano. Schweiz. Z. Hydr., Vol. 44, pp. 455–484.Google Scholar
  25. Rutter, K., Salvadè, G. and Schwab, D.J., 1983. On internal wave dynamics of the Lake of Lugano. J. Geophys. Astrophys. Fluid Dyn., in press.Google Scholar
  26. Kanari, S., 1975. The long period internal waves in Lake Biwa. Limnol. & Oceanogr., Vol. 20, pp. 544–553.CrossRefGoogle Scholar
  27. Krauss, W., 1966. Methoden und Ergebnisse der theoretischen Ozeanographie. 2. Intern. Wellen. Borntraeger, Berlin-Stuttgart.Google Scholar
  28. Krauss, W., 1973. Methods and results of theoretical oceanography. 1. Dynamics of the homogeneous and quasihomogeneous Ocean. Borntraeger, Berlin-Stuttgart.Google Scholar
  29. LeBlond, P.H. and Mysak, L.A., 1978. Waves in the Ocean. Elsevier Oceanography Series. Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York.Google Scholar
  30. Lighthill, J., 1969. Dynamic response of the Indian Ocean to outset of the southwest monsoon. Phil. Trans. Royal. Soc. London, Vol. A 265, 1159, pp. 45–92.CrossRefADSGoogle Scholar
  31. Lighthill, J., 1978. Waves in Fluids. Cambridge Uuniversity Press, Cambridge.MATHGoogle Scholar
  32. Mortimer, C.H., 1952. Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere. Phil. Trans. Royal Soc. London, Vol. B 236, pp. 355–404.CrossRefADSGoogle Scholar
  33. Mortimer, C.H., 1953. The resonant response of stratified lakes to wind. Schweiz. Z. Hydr., Vol. 15, pp. 94–151.Google Scholar
  34. Mortimer, C.H., 1963. Frontiers in physical limnology with particular reference to long waves in rotating basins. pp. 9–42. In: Proc. 5th Conf. Freat Lakes Res., Great Lakes Res. Div. Univ. Mich. Publ. 9.Google Scholar
  35. Mortimer, C.H., 1974. Lake hydrodynamics. Mitt. Int. Ver. Theor.,Angew. Limnol., 20, pp. 124–197.Google Scholar
  36. Mortimer, C.H., 1975. Substantive corrections to SIL Communications (IVL Mitteilungen) Numbers 6 and 20. Mitt. Int. Ver. Theor. Angew. Limnol., 19, pp. 60–72.Google Scholar
  37. Mortimer, C.H. and Fee, E.J., 1976. Free surface oscillations and tides of Lakes Michigan and Superior. Phil. Trans. Royal Soc. London, Vol. A 281, pp. 1–61.CrossRefADSGoogle Scholar
  38. Mortimer, C.H., 1979. Strategies for coupling data collection and analysis with dynamic modelling of lake motions. In: Lake of Hydrodyna–mics (eds. W.H. Graf & C.H. Mortimer ). Elsevier, Amsterdam, pp. 183–222.CrossRefGoogle Scholar
  39. Mühleisen, R. and Kurth, W., 1978. Experimental investigations on the seiches of Lake Constance. Schweiz. Z. Hydr., Vol. 40.Google Scholar
  40. Mysak, L.A., 1980. Recent advances in shelf wave dynamics. Reviews of Geophysics and Space Physics, Vol. 18, pp. 211–241.CrossRefADSGoogle Scholar
  41. Phillips, O.M., 1966. The Dynamics of the Upper Ocean. Cambridge University Press, Cambridge.MATHGoogle Scholar
  42. Platzman, G.W., 1972. Two-dimensional free oscillation in natural basins. J. Phys. Oceanogr., Vol. 2, pp. 117–138.CrossRefADSGoogle Scholar
  43. Platzman, G.W., 1975. Normal modes of the Atlantic and Indian Ocean. J. Phys. Oceanogr., Vol. 5, pp. 201–221.CrossRefADSGoogle Scholar
  44. Platzman, G.W. and Rao, D.B., 1964. The free oscillations of Lake Erie. Studies on Oceanography (Hidaka Volume, ed. by K. Yoshida) Tokio Univ. Press, pp. 359–382.Google Scholar
  45. Raggio, G. and Hutter, K., 1982a. An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 1: Theoretical Introduction. J. Fluid Mech., Vol. 121, pp. 231–255.CrossRefMATHADSGoogle Scholar
  46. Raggio, G. and Rutter, 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 basin with flat bottom. J. Fluid Mech., Vol. 121, pp. 257–281.CrossRefMATHADSGoogle Scholar
  47. Raggio, G. and Hutter, K., 1982c. An extended channel model for the prediction of motion in elongated homogeneous lakes. Part 3: Free oscillations in natural basins. J. Fluid Mech., Vol. 121, pp. 283–299.CrossRefMATHADSGoogle Scholar
  48. Rao, D.B., 1966. Free gravitational oscillations in rotating rectangular basins. J. Fluid Mech. 24, pp. 523–555.CrossRefADSGoogle Scholar
  49. Schwab, D.J., 1977. Internal free oscillations in Lake Ontario. Limnol.& Oceanogr., Vol. 22, pp. 700–708.MathSciNetCrossRefGoogle Scholar
  50. Schwab, D.J., 1980. The free oscillations of Lake S. Clair - An application of Lanczos’ procedure. Great Lakes Environmental Research Laboratory. No. AA, Tech. Memorandum ERL GLERL-32.Google Scholar
  51. Schwab, D.J. and Rao, D.B., 1977. Gravitational oscillations of Lake Huron, Saginow Bay, Georgian Bay, and the North Channel. J. Geophys. Research, Vol. 82, pp. 2105–2116.CrossRefADSGoogle Scholar
  52. Simons, T.J., 1980. Circulation Models of Lakes and Inland Seas. Canadian Bulletin of Fisheries and Aquatic Sciences, No. 203, Ottawa.Google Scholar
  53. Taylor, G.I., 1922. Tidal oscillations in gulfs and rectangular basins. Proc. London Math. Soc. Ser. 220, pp. 148–181.CrossRefGoogle Scholar
  54. Tison, L.J. and Tison G. Jr., 1969. Seiches et dénivellations causées par le vent dans les lacs, baies, estuaries. Note Technique No. 102, Organisation Météorologique Mondiale, Genève, Suisse.Google Scholar
  55. Turner, J.S., 1973. Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
  56. Van Dantzig, D. and Lauwerier, H.A., 1960. The North Sea problem: free oscillations of a rotating rectangular sea. Proc. K. Ned. Akad. Wet., A 63, pp. 339–354.MATHGoogle Scholar
  57. Witham, G.B., 1974. Linear and Non-linear Waves. Wiley, New York.Google Scholar
  58. Yih, C.S., 1965. Dynamics of Nonhomogeneous Fluids. MacMillan, New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Kolumban Hutter
    • 1
  1. 1.Laboratory of HydraulicsHydrology and GlaciologyZurichSwitzerland

Personalised recommendations