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Studies of Thermal Convection in a Rotating Cylinder with Some Implications for Large-Scale Atmospheric Motions

  • Dave Fultz
  • Robert R. Long
  • George V. Owens
  • Walter Bohan
  • Robert Kaylor
  • Joyce Weil
Chapter
Part of the Meteorological Monographs book series (METEOR, volume 4)

Abstract

The results of several years of research in atmospheric models are presented. A brief historical summary covers the important experimental work of early investigators in this field as well as the immediate background of the work at Chicago. The experiments are conducted in rotating cylindrical containers with various arrangements of the heat sources and sinks. A short description of the experimental apparatus and of several of the more unusual or important techniques which have evolved is presented.

To facilitate comparison to the prototype, the pertinent equations are developed in nondimensional form and the modeling criteria investigated in terms of the appropriate nondimensional parameters. Experience indicates that the most important of the controlled variables in the experiments are the rotation and heating rates. A nondimensional parameter is defined (the Rossby number, R0*) whose value roughly determines the types of motions observed.

Two principal convective regimes are found, corresponding to high and low values of the Rossby number. With a high Rossby number (Hadley regime), the motion is symmetric with the heat transport accomplished by ageostrophic components of the flow. At low Rossby numbers (Rossby regime), a wave regime is established, characterized by geostrophic heat transport. Empirical criteria for wave number changes and transition from symmetric to wave regimes in a rotating annulus are also presented.

Keywords

Rossby Number Cold Source Bunsen Burner Eddy Transport Angular Momentum Balance 
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.

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References

  1. 1.
    Abbe, C., 1907: Comprehensive maps and models of the globe for special meteorological.studies. Mon. Wea. Rev., 35, 559–564.CrossRefGoogle Scholar
  2. 2.
    Abbe, C., 1907: Projections of the globe appropriate for labora- tory methods of studying the general circulation of the atmosphere. Bull. Amer. math. Soc., (2), 13, 502–506.CrossRefGoogle Scholar
  3. 3.
    Bellamy, J. C., 1945: The use of pressure altitude and altimeter corrections in meteorology. J. Meteor., 2, 1–79.CrossRefGoogle Scholar
  4. 4.
    Bigelow, F. H., 1902: IV Review of Ferrel’s and Oberbeck’s theories of the local and general circulations. Mon. Wea. Rev., 30, 163–171, experiment p. 165.CrossRefGoogle Scholar
  5. 5.
    Birkhoff, G., 1950: Hydrodynamics: A study in logic, fact, similitude. Princeton Univ. Press, 186 pp.Google Scholar
  6. 6.
    Bjerknes, V., 1916: Über thermodynamische Maschinen die unter Mitwirkung der Schwerkraft arbeiten. Abh. sächs. Akad. Wiss., 35, Nr. 1, 33 pp.Google Scholar
  7. 7.
    Bridgman, P. W., 1931: Dimensional analysis. New Haven, Yale Univ. Press, 113 pp.Google Scholar
  8. 8.
    Chandrasekhar, S., 1953: The instability of a layer of fluid heated below and subject to Coriolis forces. Proc. r. Soc. London, (A), 217, 306–327.CrossRefGoogle Scholar
  9. 9.
    Chandrasekhar, S., and D. D. Elbert, 1955: The instability of a layer of fluid heated below and subject to Coriolis forces II. Proc. r. Soc. London, (A), 231, 198–210.Google Scholar
  10. 10.
    Charney, J., 1947: The dynamics of long waves in a baro-clinic westerly current. J. Meteor., 4, 135–163.CrossRefGoogle Scholar
  11. 11.
    Corn, J., and D. Fultz, 1955: Synoptic analyses of convection in a rotating cylinder. Geophys. Res. Pap. No. 34, AFCRC, 72 pp.Google Scholar
  12. 12.
    Davies, T. V., 1953: Large scale atmospheric flow patterns in the laboratory. Aero. Res. Coun. F. M. 1896 15, 876, 1–5.Google Scholar
  13. 13.
    Davies, T. V., 1953: The forced flow of a rotating viscous liquid which is heated from below. Philosoph. Trans. r. Soc. London, (A), 246, 81–112.CrossRefGoogle Scholar
  14. 14.
    Davies, T. V., 1956: The forced flow due to heating of a rotating liquid. Philosoph. Trans. r. Soc. London, (A), 249, 27–64.CrossRefGoogle Scholar
  15. 15.
    Dorsey, N. E., 1940: Properties of ordinary water substance. Amer. chem. Soc. Mon. No. 81, New York, Rheinhold Publishing Corp., 673 pp.Google Scholar
  16. 16.
    Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 33–52.CrossRefGoogle Scholar
  17. 17.
    Exner, F. M., 1923: Über die Bildung von Windhosen und Zyklonen. S. B. Akad. Wiss. Wien, Abt. Ila, 132, 1–16.Google Scholar
  18. 18.
    Faller, A. J., 1956: A demonstration of fronts and frontal waves in atmospheric models. J. Meteor., 13, 1–4.CrossRefGoogle Scholar
  19. 19.
    Fischer, K., 1931: Untersuchung der Strömung in einer Zentrifugalpumpe. Mitt. hydraul. Inst. de Tech. Hochsch. (Munchen), 4, 7–27.Google Scholar
  20. 20.
    Fjørtoft, R., 1950: Application of line integral theorems in deriving criteria for stability of a baroclinic circular vortex. Geofys. Publ., 17, No. 6, 52 pp.Google Scholar
  21. 21.
    Fultz, D., 1949: A preliminary report on experiments with thermally produced lateral mixing in a rotating hemispherical shell of liquid. J. Meteor., 6, 17–33.CrossRefGoogle Scholar
  22. 22.
    Fultz, D., 1950: Experimental studies of a polar vortex I. Tellus, 2, 137–149.CrossRefGoogle Scholar
  23. 23.
    Fultz, D., 1950: Experimental studies related to atmospheric flow around obstacles. Geofys. Pura e Appi., 17, 89–93.Google Scholar
  24. 24.
    Fultz, D., 1950: Experiments combining convection and rotation and some of their possible implications. Proc. Mid-West Conf. Flu. Dynam. (1st Conf.), 297–304.Google Scholar
  25. 25.
    Fultz, D., 1951: Experimental analogies to atmospheric motions. Compendium Meteor., 1235–1248.Google Scholar
  26. 26.
    Fultz, D., 1951: Non-dimensional equations and modelling criteria for the atmosphere. J. Meteor., 8, 262–267.CrossRefGoogle Scholar
  27. 27.
    Fultz, D., 1952: On the possibility of experimental models of the polar-front wave. J. Meteor., 9, 379–384.CrossRefGoogle Scholar
  28. 28.
    Fultz, D., 1956: A survey of certain thermally and mechanically driven fluid systems of meteorological interest, in Fluid models in geophysics. Proc. 1st Sympos. on the Use of Models in Geophys. Fluid Dynamics, Baltimore, Sept., 1953, 27–63.Google Scholar
  29. 29.
    Fultz, D., 1956: A fluid convection experiment of special theo- retical interest. J. Geophys. Res., 61, 328–334.Google Scholar
  30. 30.
    Fultz, D., and R. R. Long, 1951: Two-dimensional flow around a circular barrier in a rotating spherical shell. Tellus, 3, 61–68.CrossRefGoogle Scholar
  31. 31.
    Fultz, D., and P. Frenzen, 1955: A note on certain interesting ageostrophic motions in a rotating hemispherical shell. J. Meteor., 12, 332–338.CrossRefGoogle Scholar
  32. 32.
    Fultz, D., Y. Nakagawa, and P. Frenzen, 1954: An instance in thermal convection of Eddington’s “overstability”. Phys. Rev., 94, 1471–1472.CrossRefGoogle Scholar
  33. 33.
    Görtler, H., 1941: Neuere Beiträge zur Dynamik atmosphärischer and ozeanischer Strömungen. Naturwiss., 29, 473–479.CrossRefGoogle Scholar
  34. 34.
    Hadley, G., 1735: Concerning the cause of the general tradewinds. Philosoph. Trans. r. Soc., 39, 58–62.CrossRefGoogle Scholar
  35. 35.
    Halley, E., 1686: An historical account of the trade winds and monsoons, etc. Philosoph. Trans. r. Soc., 16, 153–168.CrossRefGoogle Scholar
  36. 36.
    Helmholtz, H., 1873: Über ein Theorem, geometrisch ähnlich Bewegungen flüssiger Körper betreffend, nebst Anwendung auf das Problem, Luft-ballons zu lenken. Monatsb. K. Akad. Wiss. Berlin, 501–504. (Translation in Abbe, C., 1893: The mechanics of the earth’s atmosphere. Smithsonian misc. Coll., 34, 67–77.)Google Scholar
  37. 37.
    Hide, R., 1953: Some experiments on thermal convection in a rotating liquid. Quart. J. r. Meteor. Soc., 79, 161.CrossRefGoogle Scholar
  38. 38.
    Hide, R., 1956: Fluid motion in the earth’s core and some experiments on thermal convection in a rotating liquid, in Fluid models in geophysics. Proc. 1st Sympos. on the Use of Models in Geophys. Fluid Dynamics, Baltimore, Sept. 1953, 101–116.Google Scholar
  39. 39.
    Jeffreys, H., 1925: On fluid motions produced by differences of temperature and humidity. Quart. J. r. Meteor. Soc., 51, 347–356.CrossRefGoogle Scholar
  40. 40.
    Kuo, H. L., 1953: The stability properties and structure of disturbances in a baroclinic atmosphere. J. Meteor., 10, 235–243.CrossRefGoogle Scholar
  41. 41.
    Kuo, H. L., 1954: Symmetrical disturbances in a thin layer of fluid subject to a horizontal temperature gradient and rotation. J. Meteor., 11, 399–411.CrossRefGoogle Scholar
  42. 42.
    Kuo, H. L., 1955: On convective instability of a rotating fluid with a horizontal temperature contrast. J. Marine Res., 14, 14–32.Google Scholar
  43. 43.
    Kuo, H. L., 1956: Energy-releasing processes and stability of thermally driven motions in a rotating fluid. J. Meteor., 13, 82–101.CrossRefGoogle Scholar
  44. 44.
    Kuo, H. L., 1956: Forced and free axially-symmetric convection produced by differential heating in a rotating fluid. J. Meteor., 13, 521–527.CrossRefGoogle Scholar
  45. 45.
    Kuo, H. L., 1956: On convective instability of a rotating fluid, in Fluid models in geophysics. Proc. 1st Sympos. on the Use of Models in Geophys. Fluid Dynamics, Baltimore, 65–72.Google Scholar
  46. 46.
    Langhaar, H. L., 1951: Dimensional analysis and theory of models. New York, J. Wiley and Sons, 177 pp.Google Scholar
  47. 47.
    Long, R. R., 1951: A theoretical and experimental study of the motion and stability of certain atmospheric vortices, J. Meteor., 8, 207–221.CrossRefGoogle Scholar
  48. 48.
    Long, R. R., 1952: The flow of a liquid past a barrier in a rotating spherical shell. J. Meteor., 9, 187–199.CrossRefGoogle Scholar
  49. 49.
    Long, R. R., 1953: Steady motion around a symmetrical obstacle moving along the axis of a rotating fluid. J. Meteor., 10, 197–203.CrossRefGoogle Scholar
  50. 50.
    Long, R. R., 1954: Note on Taylor’s “Ink Walls” in a rotating fluid. J. Meteor., 11, 247–249.CrossRefGoogle Scholar
  51. 51.
    Lorenz, E. N., 1952: Flow of angular momentum as a predictor for the zonal westerlies. J. Meteor., 9, 152–157.CrossRefGoogle Scholar
  52. 52.
    Lorenz, E. N., 1956: A proposed explanation for the existence of two regimes of flow in a rotating symmetrically-heated cylindrical vessel, in Fluid models in geophysics. Proc. 1st Sympos. on the Use of Models in Geophys. Fluid Dynamics, Baltimore, 73–80.Google Scholar
  53. 53.
    Mach, E., 1942: The science of mechanics. La Salle, Ill., Open Court Publ., 635 pp. (see p. 199 ff.).Google Scholar
  54. 54.
    Mintz, Y., 1955: Final computation of the mean geostrophic poleward flux of angular momentum and of sensible heat in the winter and summer of 1949. Final Report, Contract AF 19(122)-48, UCLA.Google Scholar
  55. 55.
    Mintz, Y., and S.-K. Kao, 1952: A zonal-index tendency equation and its application to forecasts of the zonal index. J. Meteor., 9, 87–92.CrossRefGoogle Scholar
  56. 56.
    Montgomery, R. B., 1937: A suggested method for representing gradient flow in isentropic surfaces. Bull. Amer. meteor. Soc., 18, 210–212.Google Scholar
  57. 57.
    Nakagawa, Y., and P. Frenzen, 1955: A theoretical and experimental study of cellular convection in rotating fluids. Tellus, 7, 1–21.CrossRefGoogle Scholar
  58. 58.
    Namias, J., 1954: Quasi-periodic cyclogenesis in relation to the general circulation. Tellus, 6, 8–22.CrossRefGoogle Scholar
  59. 59.
    Palmén, E., and K. Nagler, 1948: An analysis of the wind and temperature over North America in a case of approximately westerly flow. J. Meteor., 5, 58–64.CrossRefGoogle Scholar
  60. 60.
    Petterssen, S., and W. C. Swinbank, 1947: On the application of the Richardson criterion to large-scale turbulence in the free atmosphere. Quart. J. r. Meteor. Soc., 73, 335–345.CrossRefGoogle Scholar
  61. 61.
    Prandtl, L., 1939: Beiträge zur Mechanik der Atmosphäre. P. V. Meteor. Un. geod. geophys. int., Edinbourg, 1936, II.Google Scholar
  62. 62.
    Prandtl, L., 1952: Führer durch die strömungslehre. 3rd ed. Braunschweig, F. Vieweg, 382 pp.Google Scholar
  63. 63.
    Reynolds, O., 1883: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and, of the law of resistance in parallel channels. Paps. on mech. Phys. Subj. 2, 51–105, (Philosoph. Trans. r. Soc. London (A), 174 935).Google Scholar
  64. 64.
    Reynolds, O., 1893: Study of fluid motion by means of coloured bands. Paps. on mech. Phys. Subj. 2, 524–534, (Proc. r. Inst. Gt. Brit. 524–534).Google Scholar
  65. 65.
    Riehl, H., T. C. Yeh, and N. E. La Seur, 1950: A study of variations of the general circulation. J. Meteor., 7, 181–194.CrossRefGoogle Scholar
  66. 66.
    Riehl, H., 1952: Forecasting in middle latitudes. Meteor. Monogr., 1, No. 5, 80 pp.Google Scholar
  67. 67.
    Rogers, M. H., 1954: The forced flow of a thin layer of viscous fluid on a rotating sphere. Proc. r. Soc. London, (A), 224, 192–208.CrossRefGoogle Scholar
  68. 68.
    Rossby, C.-G., 1926: On the solution of problems of atmospheric motion by means of model experiments. Mon. Wea. Rev., 54, 237–240.CrossRefGoogle Scholar
  69. 69.
    Rossby, C.-G., 1928: Studies in the dynamics of the stratosphere. Beitr. Phys. frei Atmos., 14, 240–265 (see p. 261 ).Google Scholar
  70. 70.
    Rossby, C.-G., 1947: On the distribution of angular velocity in gaseous envelopes under the influence of large-scale horizontal mixing processes. Bull. Amer. meteor. Soc., 28, 53–68.Google Scholar
  71. 71.
    Runcorn, S. K., 1954: The earth’s core. Trans. Amer. geophys. Union, 35, 49–63.CrossRefGoogle Scholar
  72. 72.
    Sabin, B. A., 1954: A qualitative study of some of the critical parameters for the “dishpan” model of the atmosphere. Mass. Inst. Tech., B.Sc. thesis.Google Scholar
  73. 73.
    Sandstrom, J. W., 1919: The hydrodynamics of Canadian Atlantic waters, Canadian Fisheries expedition, 1914–1915. Ottawa, Dept. of Naval Service, 221–343.Google Scholar
  74. 74.
    Skeib, G., 1953: Modellversuche zur thermischen konvektion. Abh. Met. Hydro. Dienst., 3, 1–56.Google Scholar
  75. 75.
    Starr, V. P., and R. R. Long, 1953: The flux of angular momentum in rotating model experiments. Geophys. Res. Pap. No. 24, AFCRC, 103–113.Google Scholar
  76. 76.
    Starr, V. P., 1954: Commentaries concerning research on the general circulation. Tellus, 6, 268–272.CrossRefGoogle Scholar
  77. 77.
    Starr, V. P., and R. M. White, 1951: A hemispherical study of the atmospheric angular momentum balance. Quart. J. r. Meteor. Soc., 77, 215–225.CrossRefGoogle Scholar
  78. Starr, V. P., 1954: Balance requirements of the general circulation. Geophys. Res. Pap. No. 35, AFCRC, 57 pp.Google Scholar
  79. 79.
    Taylor, G. I., 1921: Experiments with rotating fluids. Proc. Cambridge Philosoph. Soc., 20, 326–329.Google Scholar
  80. 80.
    Taylor, G. I., 1923: Experiments on the motion of solid bodies in rotating fluids. Proc. r. Soc. London, (A), 104, 213–218.CrossRefGoogle Scholar
  81. 81.
    Thiriot, K. H., 1940: Über die laminare Anlaufströmung einer Flüssigkeit über einem rotierenden Boden bei plötzlicher Änderung des Drehungszustandes. Z. Angew. Math. Mech., 20, 1–13.CrossRefGoogle Scholar
  82. 82.
    Thomson, J., 1892, 1857: On the grand currents of atmospheric circulation. Philosoph. Trans. r. Soc. London, (A), 183, 653–684, (1892); Rep. Brit. Assoc., 27, 38–39, (1857).Google Scholar
  83. 83.
    Univ. of Chicago, Dept. Meteor., 1947: On the general circulation of the atmosphere in middle latitudes. Bull. Amer. meteor. Soc., 28, 225–280.Google Scholar
  84. 84.
    Vettin, F., 1857: Über den aufsteigenden Luftstrom, die Entstehung des Hagels und der Wirbel-Stürme. Ann. Phys., Lpz., (2), 102, 246–255.CrossRefGoogle Scholar
  85. 85.
    Vettin, F., 1884: Experimentelle Darstellung von Luftbewegungen unter dem Einfluss von Temperatur-Unterschieden und Rotations-Impulsen. Z. Meteor., 1, 227–230, 271–276; (1885) 2, 172–183.Google Scholar
  86. 86.
    von Arx, W. S., 1952: A laboratory study of the wind driven ocean circulation. Tellus, 4, 311–318.CrossRefGoogle Scholar
  87. 87.
    von Arx, W. S., 1955: An experimental study of the dependence of the primary ocean circulation on the mean zonal wind field. Mass. Inst. Tech., Sc. D. thesis.Google Scholar
  88. 88.
    von Bezold, W., 1884: Ueber Strömungsfiguren in Flüssigkeiten. K. bair. Acad. Wiss., 4, 569–593.Google Scholar
  89. 89.
    von Bezold, W., 1887: Experimentaluntersuchungen über rotirende Flüssigkeiten. Ann. Phys. und Chem., (3), 32, 171–187.CrossRefGoogle Scholar
  90. 90.
    Wortman, F. X., 1953: Eine Methode zur Beobachtung und Messung von Wasserströmungen mit Tellur. Z. f. Angew. Physik, 5, 201–206.Google Scholar

Copyright information

© American Meteorological Society 1959

Authors and Affiliations

  • Dave Fultz
    • 1
  • Robert R. Long
    • 1
    • 2
  • George V. Owens
    • 1
    • 3
  • Walter Bohan
    • 1
    • 4
  • Robert Kaylor
    • 1
  • Joyce Weil
    • 1
  1. 1.Hydrodynamics Laboratory, Department of MeteorologyUniversity of ChicagoUSA
  2. 2.Johns Hopkins UniversityUSA
  3. 3.North American Aircraft Co.Los AngelesUSA
  4. 4.Cook Research LaboratoriesChicagoUSA

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